{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Naive Bayes Classification using Wine data (UCI ML Repo)\n",
    "\n",
    "The [Naive Bayes Classifier](http://dataaspirant.com/2017/02/06/naive-bayes-classifier-machine-learning/) technique is based on the so-called Bayesian theorem and is particularly suited when the dimensionality of the inputs is high. Despite its simplicity, Naive Bayes can often outperform more sophisticated classification methods.\n",
    "\n",
    "### Bayes' Theorem\n",
    "\n",
    "The algorithm is based on the famous [___Bayes theorem___](https://en.wikipedia.org/wiki/Bayes%27_theorem) named after Rev. Thomas Bayes. It works on conditional probability. [Conditional probability](https://en.wikipedia.org/wiki/Conditional_probability) is the probability that something will happen, given that something else has already occurred. Using the conditional probability, we can calculate the probability of an event using its prior knowledge.\n",
    "\n",
    "Bayes' theorem is stated mathematically as the following equation:\n",
    "\n",
    "$${\\displaystyle P(A\\mid B)={\\frac {P(B\\mid A)\\,P(A)}{P(B)}},}$$\n",
    "where $A$ and $B$ are events and $P(B)\\neq{0}$.\n",
    "\n",
    "$P(A\\mid B)$ is a [conditional probability](https://en.wikipedia.org/wiki/Conditional_probability): the likelihood of event $A$ occurring given that $B$ is true.\n",
    "\n",
    "$P(B\\mid A)$ is also a conditional probability: the likelihood of event $B$ occurring given that $A$ is true.\n",
    "\n",
    "$P(A)$ and $P(B)$ are the probabilities of observing $A$ and $B$ independently of each other; this is known as the [marginal probability](https://en.wikipedia.org/wiki/Marginal_probability).\n",
    "\n",
    "### What's _Naive_ in Naive Bayes and why is it a super fast algorithm?\n",
    "\n",
    "It is called naive Bayes or idiot Bayes because the calculation of the probabilities for each hypothesis are simplified to make their calculation tractable. Rather than attempting to calculate the values of each attribute value, they are assumed to be conditionally independent given the target value.\n",
    "\n",
    "This is a very strong assumption that is most unlikely in real data, i.e. that the attributes do not interact. Nevertheless, the approach performs surprisingly well on data where this assumption does not hold.\n",
    "\n",
    "Training is fast because only the probability of each class and the probability of each class given different input values need to be calculated. **No coefficients need to be fitted by optimization procedures.**\n",
    "\n",
    "The class probabilities are simply the frequency of instances that belong to each class divided by the total number of instances. The conditional probabilities are the frequency of each attribute value for a given class value divided by the frequency of instances with that class value.\n",
    "\n",
    "### Data analyzed in this notebook\n",
    "\n",
    "In this notebook, we will show how to use Python scikit-learn's Naive Bayes method to classify origin of wine based on physio-chemical analysis data. These data are the results of a chemical analysis of wines grown in the same region in Italy but derived from three different cultivars. The analysis determined the quantities of 13 constituents found in each of the three types of wines.\n",
    "\n",
    "Details can be [**found here**](http://archive.ics.uci.edu/ml/datasets/Wine)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read in the data and perform basic exploratory analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Class</th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malic acid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Alcalinity of ash</th>\n",
       "      <th>Magnesium</th>\n",
       "      <th>Total phenols</th>\n",
       "      <th>Flavanoids</th>\n",
       "      <th>Nonflavanoid phenols</th>\n",
       "      <th>Proanthocyanins</th>\n",
       "      <th>Color intensity</th>\n",
       "      <th>Hue</th>\n",
       "      <th>OD280/OD315 of diluted wines</th>\n",
       "      <th>Proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "      <td>2.29</td>\n",
       "      <td>5.64</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.92</td>\n",
       "      <td>1065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.28</td>\n",
       "      <td>4.38</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.40</td>\n",
       "      <td>1050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "      <td>2.81</td>\n",
       "      <td>5.68</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "      <td>2.18</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.86</td>\n",
       "      <td>3.45</td>\n",
       "      <td>1480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "      <td>1.82</td>\n",
       "      <td>4.32</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.93</td>\n",
       "      <td>735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>14.20</td>\n",
       "      <td>1.76</td>\n",
       "      <td>2.45</td>\n",
       "      <td>15.2</td>\n",
       "      <td>112</td>\n",
       "      <td>3.27</td>\n",
       "      <td>3.39</td>\n",
       "      <td>0.34</td>\n",
       "      <td>1.97</td>\n",
       "      <td>6.75</td>\n",
       "      <td>1.05</td>\n",
       "      <td>2.85</td>\n",
       "      <td>1450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>14.39</td>\n",
       "      <td>1.87</td>\n",
       "      <td>2.45</td>\n",
       "      <td>14.6</td>\n",
       "      <td>96</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2.52</td>\n",
       "      <td>0.30</td>\n",
       "      <td>1.98</td>\n",
       "      <td>5.25</td>\n",
       "      <td>1.02</td>\n",
       "      <td>3.58</td>\n",
       "      <td>1290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1</td>\n",
       "      <td>14.06</td>\n",
       "      <td>2.15</td>\n",
       "      <td>2.61</td>\n",
       "      <td>17.6</td>\n",
       "      <td>121</td>\n",
       "      <td>2.60</td>\n",
       "      <td>2.51</td>\n",
       "      <td>0.31</td>\n",
       "      <td>1.25</td>\n",
       "      <td>5.05</td>\n",
       "      <td>1.06</td>\n",
       "      <td>3.58</td>\n",
       "      <td>1295</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>14.83</td>\n",
       "      <td>1.64</td>\n",
       "      <td>2.17</td>\n",
       "      <td>14.0</td>\n",
       "      <td>97</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.98</td>\n",
       "      <td>0.29</td>\n",
       "      <td>1.98</td>\n",
       "      <td>5.20</td>\n",
       "      <td>1.08</td>\n",
       "      <td>2.85</td>\n",
       "      <td>1045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>13.86</td>\n",
       "      <td>1.35</td>\n",
       "      <td>2.27</td>\n",
       "      <td>16.0</td>\n",
       "      <td>98</td>\n",
       "      <td>2.98</td>\n",
       "      <td>3.15</td>\n",
       "      <td>0.22</td>\n",
       "      <td>1.85</td>\n",
       "      <td>7.22</td>\n",
       "      <td>1.01</td>\n",
       "      <td>3.55</td>\n",
       "      <td>1045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Class  Alcohol  Malic acid   Ash  Alcalinity of ash  Magnesium  \\\n",
       "0      1    14.23        1.71  2.43               15.6        127   \n",
       "1      1    13.20        1.78  2.14               11.2        100   \n",
       "2      1    13.16        2.36  2.67               18.6        101   \n",
       "3      1    14.37        1.95  2.50               16.8        113   \n",
       "4      1    13.24        2.59  2.87               21.0        118   \n",
       "5      1    14.20        1.76  2.45               15.2        112   \n",
       "6      1    14.39        1.87  2.45               14.6         96   \n",
       "7      1    14.06        2.15  2.61               17.6        121   \n",
       "8      1    14.83        1.64  2.17               14.0         97   \n",
       "9      1    13.86        1.35  2.27               16.0         98   \n",
       "\n",
       "   Total phenols  Flavanoids  Nonflavanoid phenols  Proanthocyanins  \\\n",
       "0           2.80        3.06                  0.28             2.29   \n",
       "1           2.65        2.76                  0.26             1.28   \n",
       "2           2.80        3.24                  0.30             2.81   \n",
       "3           3.85        3.49                  0.24             2.18   \n",
       "4           2.80        2.69                  0.39             1.82   \n",
       "5           3.27        3.39                  0.34             1.97   \n",
       "6           2.50        2.52                  0.30             1.98   \n",
       "7           2.60        2.51                  0.31             1.25   \n",
       "8           2.80        2.98                  0.29             1.98   \n",
       "9           2.98        3.15                  0.22             1.85   \n",
       "\n",
       "   Color intensity   Hue  OD280/OD315 of diluted wines  Proline  \n",
       "0             5.64  1.04                          3.92     1065  \n",
       "1             4.38  1.05                          3.40     1050  \n",
       "2             5.68  1.03                          3.17     1185  \n",
       "3             7.80  0.86                          3.45     1480  \n",
       "4             4.32  1.04                          2.93      735  \n",
       "5             6.75  1.05                          2.85     1450  \n",
       "6             5.25  1.02                          3.58     1290  \n",
       "7             5.05  1.06                          3.58     1295  \n",
       "8             5.20  1.08                          2.85     1045  \n",
       "9             7.22  1.01                          3.55     1045  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('./Datasets/wine.data.csv')\n",
    "df.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Basic statistics of the features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malic acid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Alcalinity of ash</th>\n",
       "      <th>Magnesium</th>\n",
       "      <th>Total phenols</th>\n",
       "      <th>Flavanoids</th>\n",
       "      <th>Nonflavanoid phenols</th>\n",
       "      <th>Proanthocyanins</th>\n",
       "      <th>Color intensity</th>\n",
       "      <th>Hue</th>\n",
       "      <th>OD280/OD315 of diluted wines</th>\n",
       "      <th>Proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "      <td>178.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>13.000618</td>\n",
       "      <td>2.336348</td>\n",
       "      <td>2.366517</td>\n",
       "      <td>19.494944</td>\n",
       "      <td>99.741573</td>\n",
       "      <td>2.295112</td>\n",
       "      <td>2.029270</td>\n",
       "      <td>0.361854</td>\n",
       "      <td>1.590899</td>\n",
       "      <td>5.058090</td>\n",
       "      <td>0.957449</td>\n",
       "      <td>2.611685</td>\n",
       "      <td>746.893258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.811827</td>\n",
       "      <td>1.117146</td>\n",
       "      <td>0.274344</td>\n",
       "      <td>3.339564</td>\n",
       "      <td>14.282484</td>\n",
       "      <td>0.625851</td>\n",
       "      <td>0.998859</td>\n",
       "      <td>0.124453</td>\n",
       "      <td>0.572359</td>\n",
       "      <td>2.318286</td>\n",
       "      <td>0.228572</td>\n",
       "      <td>0.709990</td>\n",
       "      <td>314.907474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>11.030000</td>\n",
       "      <td>0.740000</td>\n",
       "      <td>1.360000</td>\n",
       "      <td>10.600000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.340000</td>\n",
       "      <td>0.130000</td>\n",
       "      <td>0.410000</td>\n",
       "      <td>1.280000</td>\n",
       "      <td>0.480000</td>\n",
       "      <td>1.270000</td>\n",
       "      <td>278.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>12.362500</td>\n",
       "      <td>1.602500</td>\n",
       "      <td>2.210000</td>\n",
       "      <td>17.200000</td>\n",
       "      <td>88.000000</td>\n",
       "      <td>1.742500</td>\n",
       "      <td>1.205000</td>\n",
       "      <td>0.270000</td>\n",
       "      <td>1.250000</td>\n",
       "      <td>3.220000</td>\n",
       "      <td>0.782500</td>\n",
       "      <td>1.937500</td>\n",
       "      <td>500.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>13.050000</td>\n",
       "      <td>1.865000</td>\n",
       "      <td>2.360000</td>\n",
       "      <td>19.500000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>2.355000</td>\n",
       "      <td>2.135000</td>\n",
       "      <td>0.340000</td>\n",
       "      <td>1.555000</td>\n",
       "      <td>4.690000</td>\n",
       "      <td>0.965000</td>\n",
       "      <td>2.780000</td>\n",
       "      <td>673.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>13.677500</td>\n",
       "      <td>3.082500</td>\n",
       "      <td>2.557500</td>\n",
       "      <td>21.500000</td>\n",
       "      <td>107.000000</td>\n",
       "      <td>2.800000</td>\n",
       "      <td>2.875000</td>\n",
       "      <td>0.437500</td>\n",
       "      <td>1.950000</td>\n",
       "      <td>6.200000</td>\n",
       "      <td>1.120000</td>\n",
       "      <td>3.170000</td>\n",
       "      <td>985.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>14.830000</td>\n",
       "      <td>5.800000</td>\n",
       "      <td>3.230000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>162.000000</td>\n",
       "      <td>3.880000</td>\n",
       "      <td>5.080000</td>\n",
       "      <td>0.660000</td>\n",
       "      <td>3.580000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>1.710000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>1680.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Alcohol  Malic acid         Ash  Alcalinity of ash   Magnesium  \\\n",
       "count  178.000000  178.000000  178.000000         178.000000  178.000000   \n",
       "mean    13.000618    2.336348    2.366517          19.494944   99.741573   \n",
       "std      0.811827    1.117146    0.274344           3.339564   14.282484   \n",
       "min     11.030000    0.740000    1.360000          10.600000   70.000000   \n",
       "25%     12.362500    1.602500    2.210000          17.200000   88.000000   \n",
       "50%     13.050000    1.865000    2.360000          19.500000   98.000000   \n",
       "75%     13.677500    3.082500    2.557500          21.500000  107.000000   \n",
       "max     14.830000    5.800000    3.230000          30.000000  162.000000   \n",
       "\n",
       "       Total phenols  Flavanoids  Nonflavanoid phenols  Proanthocyanins  \\\n",
       "count     178.000000  178.000000            178.000000       178.000000   \n",
       "mean        2.295112    2.029270              0.361854         1.590899   \n",
       "std         0.625851    0.998859              0.124453         0.572359   \n",
       "min         0.980000    0.340000              0.130000         0.410000   \n",
       "25%         1.742500    1.205000              0.270000         1.250000   \n",
       "50%         2.355000    2.135000              0.340000         1.555000   \n",
       "75%         2.800000    2.875000              0.437500         1.950000   \n",
       "max         3.880000    5.080000              0.660000         3.580000   \n",
       "\n",
       "       Color intensity         Hue  OD280/OD315 of diluted wines      Proline  \n",
       "count       178.000000  178.000000                    178.000000   178.000000  \n",
       "mean          5.058090    0.957449                      2.611685   746.893258  \n",
       "std           2.318286    0.228572                      0.709990   314.907474  \n",
       "min           1.280000    0.480000                      1.270000   278.000000  \n",
       "25%           3.220000    0.782500                      1.937500   500.500000  \n",
       "50%           4.690000    0.965000                      2.780000   673.500000  \n",
       "75%           6.200000    1.120000                      3.170000   985.000000  \n",
       "max          13.000000    1.710000                      4.000000  1680.000000  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.iloc[:,1:].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Boxplots by output labels/classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dg//Ht1oXpzdXAfcFrkhya5JbgQOAE5Nc1kH9kiR1oovTm/8AfHDWcx+nucZ3Sgf1S5LU\niVHH6S1JcmiSQ9vX7N9u719VV1XVRYMPmrs3r6yqi7dn46Wd3fr16zn44IN55CMfycEHH8z69evH\n3SRpURu1p7cc2DCwvaZ9rKO5niepY+vXr+eEE07g1FNP5bbbbuNOd7oTRx11FACrV68ec+ukxWnU\ncXpTVZUhjyPnKH9gVb2+05ZKPbN27VpOPfVUDj/8cHbddVcOP/xwTj31VNauXTvupkmLlqssSBNq\n48aNrFix4g7PrVixgo0bHQorLZShJ02oZcuWcf7559/hufPPP59ly5aNqUXS4mfoSRPqhBNO4Kij\njmLDhg3ceuutbNiwgaOOOooTTjhh3E2TFi2XFpIm1MzNKscccwwbN25k2bJlrF271ptYpG1g6EkT\nbPXq1axevdoZWaSOGHrbYK9lx3PIuuO7rXRdd1XttQygu0VuJWmxM/S2wY0bX+fK6ZK0iHgjizTB\nnJFF6pY9PWlCOSOL1D17etKEckYWqXuGnjShnJFF6p6hJ00oZ2SRumfoSRPKGVmk7nkjizShnJFF\n6p6hJ00wZ2SRuuXpTUlSbxh60gRzcLrULU9vShPKwelS9ww9aUINDk6fuaZ36qmncswxxxh6i9RD\n1nyC6zff0mmdXc6xu/fuu3HhKx7dWX2TyNCTJpSD03c+12++xUnqx8xretKEcnC61D1DT5pQDk6X\nuufpTWlCOThd6p6hJ00wB6dL3TL0tlHnF37P6fZOLEnS7Qy9bdDlXVjQBGjXdUqSbueNLJKk3rCn\nJ41Jku1Sb1Vtl3qlnYE9PWlMqmrkxwHHfWzkspLmZuhJknrD0JMk9YahJ0nqDUNPktQbhp4kqTcM\nPUlSbxh6kqTecHC6JO0gey07nkPWHd9tpeu6q2qvZQA791SIhp4k7SA3bnydK6ePmac3JUm9YehJ\nknpjpNBLsjLJGUkuT1JJjpy1/9VJvp7kpiTXJvlUkt/YLi2WJGmBRu3pLQEuAo4FNg/ZfzHwAuAQ\nYAXwXeCcJEu7aKQkSV0Y6UaWqjobOBsgyWlD9p8+uJ3kRcBRwKHAx7e5lZIkdaDza3pJ7gwcDdwA\nfKXr+iVJWqjOhiwkOQJ4L7AHcAXwqKr6/hxlj6YJRpYuXcrU1FRXzVj0/FloLh4bO4cu/x2np6c7\nPy529uOsy3F6G2hOZ+4DPBd4f5LDquqK2QWr6mTgZIDly5dXl+NMFrVzzup0zI12Ih4bO4eO/x27\nHqfXh+Oss9ObVXVTVX2rqj5fVUcBtwDP6ap+SZK21fYcp7cLcJftWL8kSVtlpNObSZYAB7WbuwD7\nJzkUuAa4DngJcCbNtbx70wxfuD/w/q4bLEnSQo3a01sOfLl97A6sab9/FXAr8MvAh4Fv0oTfvYCV\nVfXVrhssSdJCjTpObwrIPEV+r5PWSJK0HTn3piSpN1xaaAdI5uskzyp74mjlqmqBrZGk/rKntwNU\n1UiPDRs2jFxWkrT17OlJ0g7U+UKt53RX396779ZZXZPK0JOkHaTLVdOhCdCu69zZeXpTktQbhp4k\nqTcMPUlSbxh6kqTeMPQkSb1h6EmSesPQkyT1hqEnSeoNQ0+S1BuGniSpNww9SVJvGHqSpN4w9CRJ\nveEqC1LHHrLmE1y/+ZbO6+1ySZq9d9+NC1/x6M7qkxYLQ0/q2PWbb+l8uZepqSlWrVrVWX2dr+km\nLRKe3pQk9YahJ0nqDUNPktQbhp4kqTcMPUlSbxh6kqTeMPQkSb1h6EmSesPQkyT1hqEnSeoNpyGT\nOrbXsuM5ZN3x3Ve8rruq9loG0O1UadJiYOhJHbtx4+uce1OaUJ7elCT1hqEnSeoNQ0+S1Bte05Ok\nCZNk9LInjlauqhbYmp2LPT1JmjBVNdJjw4YNI5dVw9CTJPWGoSdJ6g1DT5LUG4aeJKk3Rgq9JCuT\nnJHk8iSV5MiBfbslOTHJV5PclOSKJO9Jsv92a7UkSQswak9vCXARcCyweda+PYCHAWvbr78LPAA4\nJ4lDIiRJE2OkUKqqs4GzAZKcNmvf9cCjBp9L8jzga8Ay4N+7aKgkSdtqe13Tu1v79drtVL8kSVut\n89OPSe4MvAE4s6oum6PM0cDRAEuXLmVqaqrrZixK09PT/ix2El3/O26PY8NjbfHzd8bW6zT02mt4\npwN3B54wV7mqOhk4GWD58uXV5ZIpi1nXy8doTM45q/N/x86Pje3QRu14/s7Yep2FXht464FDgFVV\ndXVXdUuS1IVOQi/JbsB7gYNpAu/KLuqVJKlLI4VekiXAQe3mLsD+SQ4FrgE2AR8AfhV4PFBJ9m3L\nXl9Vs4c4SDu97bIy+Tnd1bn37rt1Vpe0mIza01sObBjYXtM+1gGvpBmbB3DBrNc9Gzht4c2TFp9L\nXve4zus88Piztku9Ut+MOk5vCphvgafRF3+SJGlMnHtTktQbhp4kqTcMPUlSbxh6kqTeMPQkSb1h\n6EmSesPQkyT1hqEnSeoNQ0+S1BuGniSpNww9SVJvGHqSpN4w9CRJvWHoSZJ6w9CTJPWGoSdJ6g1D\nT5LUG4aeJKk3DD1JUm8YepKk3jD0JEm9YehJknrD0JMk9YahJ0nqDUNPktQbhp4kqTcMPUlSbxh6\nkqTeMPQkSb1h6EmSesPQkyT1hqEnSeoNQ0+S1BuGniSpNww9SVJvGHqSpN4w9CRJvWHoSZJ6w9CT\nJPWGoSdJ6g1DT5LUGyOFXpKVSc5IcnmSSnLkrP2/n+TjSX7Q7l+1PRorSdK2GLWntwS4CDgW2Dxk\n/57AZ4EXddQuSZI6t+soharqbOBsgCSnDdn/rnbfPl02TtqZJdm68ieOVq6qFtAaqR+8pieNSVWN\n/NiwYcPIZSXNbaSeXteSHA0cDbB06VKmpqbG0YyJMz097c9CQ3lsaBiPi603ltCrqpOBkwGWL19e\nq1atGkczJs7U1BT+LDSMx4aG8bjYep7elCT1hqEnSeqNkU5vJlkCHNRu7gLsn+RQ4Jqq+s8k9wT2\nB+7eljkoyXXAlVV1ZdeNliRpIUbt6S0Hvtw+dgfWtN+/qt3/hHZ7Q7t9Srv9/M5aKknSNhp1nN4U\nMOegoqo6DTitkxZJkrSdeE1PktQbGfdg1iQ/AL431kZMjn2AH467EZpIHhsaxuPidgdU1b23VGjs\noafbJflSVS0fdzs0eTw2NIzHxdbz9KYkqTcMPUlSbxh6k+XkcTdAE8tjQ8N4XGwlr+lJknrDnp4k\nqTcMPUlSbxh6kqTeMPTGLMnKJGckuTxJJTly3G3S+CV5aZIvJrkhyQ+SnJnk4HG3S+OX5AVJvtoe\nGzck+VySx427XYuFoTd+S4CLgGOBzWNuiybHKuAfgN8Afgu4Ffhku6KJ+u0y4DjgYTSLAXwa+EiS\nXxlrqxYJ796cIEmmgRe2E3hLP9Uu73U98MSqOnPc7dFkSXIN8NKqeuu42zLpRlplQdLY7UVzZuba\ncTdEkyPJnYAn05wx+uyYm7MoGHrS4nAS8BXgc+NuiMYvySE0x8JdgWng96rq38fbqsXB0JMmXJI3\nAiuAFVV127jbo4lwMXAosDfwJGBdklVVddF4mzX5DD1pgiV5E/A04PCq+s6426PJUFU/Br7Vbl6Q\n5FeB/wscNb5WLQ6GnjShkpwEPJUm8L4+7vZoou0C3GXcjVgMDL0xa+/KO6jd3AXYP8mhwDVV9Z/j\na5nGKcnfA88Enghcm2Tfdtd0VU2Pr2UatySvA84CLqW5wenpNENcHKs3AocsjFmSVcCGIbvWVdWR\nO7Y1mhRJ5vqPuaaqXrkj26LJkuQ04HBgX5phLF8F/qaqPj7Odi0Whp4kqTeckUWS1BuGniSpNww9\nSVJvGHqSpN4w9CRJvWHoSZJ6w9BTLyVZ3S7au3LW80vb578/5DUvaPcd3G6fluSSHdTk2W3ZLckf\nJ/nXJNcluTnJd5O8PclDB8pNJZkaRxulSWToqa/Oa7+unPX8SuC/gPsk+cUh+64GvtZuvxr4ve3W\nwjkk2RP4FPAG4P8DzwAeDbwGOJBmUVFJQzgNmXqpqi5P8m2Gh96ngWXt94NzXj4COL/aGR2q6ts7\noq1DnAQ8HFhVVYNLDZ0LnJrkieNpljT57Ompz84DDksy+MffSuAzwPkMBGKSXwDuSxMsM8/d4fRm\nkgPb05/PS/KqJFe0px7PTHL/2W+e5OgkFyb5UZIfJjk1yT3na3CS+wLPAk6ZFXg/VVUfmef1d03y\npiQXJZlOcmXbvl+cVW7fJOuSbGpPnV6R5GNJ7tPu3zXJq5N8e6D95ydZMV/7pXEz9NRn59GsOP0w\ngCR3Bw6mCb3P0PTsZqwceM2WvJRmEvE/BI4FDgNOHyzQThr898AngScAfw78NvDP7WrYczmc5gzN\nGSO0Y5i7AHcDXgscAfwRzUKknxuY1BrgXW27/xx4FPAnwGXAHu3+42iWsvlb4DHAs2lOuc4b2tK4\neXpTfTbTa1tJc23sEcDNwAU01+72T3JgVV3SlrmBZvXyLbmkqp4+s5Hk3sDfJNmvqjYlOZAmTNZU\n1asGyn2Dpof5eGCu3toD2q/fG+UDzlZV1zOw5lobsB8Hvg+sBt7U7joMeFlVvXvg5R8Y+P4w4BNV\nddLAc2cupE3SjmRPT71VVd+l6b3M9OJWAl+oqh9X1TeAq2bt+9cRVy4/e9b2v7df92+/Porm/967\n29OEu7anWL8A3MjPXmfsVJKnJPlCkuuAW4GbaHq8Dx4o9kXgz5Mcm+SQJJlVzReBxyZZm2RFkjtv\nzzZLXTH01HfnASvaX+oz1/NmnA+sbK/HHchopzYBrpm1fXP79a7t1/u0X78F3DLrsRdwr3nqvrT9\nesCIbbmDJI8H3gdspFmH7eHArwI/GGgfNIvXngG8hGbpmsuTvDzJzO+MvwJeQXNq9jPA1UnekWSf\nhbRL2lE8vam+O5fml/+v01zb+4uBfZ8B/hj4zXZ71NDbkqvbr48Grp1n/zBTwG00p0A/sYD3fhrw\nrcG1GpPsxqxrcVV1FfAC4AVJHkxz88wamnB8S1XdApwInNheCzwCeCPNNb+nLqBd0g5hT099NxNk\nxwMBBu+IPB/4BeApNGP3vtjRe/4L8BNg/6r60pDHd+d6YVVtAk4Djk5y2LAyWxiysAfNKc1BzwTm\nvHmmqi6uqpfRBPTBQ/ZfWVVvo7kp52f2S5PEnp56raq+nuQqmp7TBVU1PbD7y8B0u29D27vp4j2/\nneRE4M1tL+pc4Ec0N6k8CnhbVW2Yp4o/BR4EfCrJP9KEzTTwQJqB6suZ+0aYc4AnJnkT8LG27DHA\ndTMFkuzd1vlumnGKtwC/C9yDtneZ5KPAhcC/0YThQ2nuPn3r1vwspB3N0JOa3t6TuOP1PKrqtiSf\nowmirk5tztT9siQbaU8hAkVzve5TwDe38NrpJI8EjqYJuefQXI+7vH39i+d5+Sk04fqHwPNoeq+P\nBz48UOZHNGH2XJprhz8BLgaeUVUfbcucBzy5bfsewH8Cfw2s3fKnl8Yn7eQSkiTt9LymJ0nqDUNP\nktQbhp4kqTcMPUlSbxh6kqTeMPQkSb1h6EmSesPQkyT1xn8Dhj063R5MKAkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb087f7630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NzKwQnNDMzKwQqmpylDQd2D17uRXwWkl7Ao9FxP80KjgzM7NqVVtDmwPcmj22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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb0b5968d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb05bcdd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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WS1olqSTpHaMSsVlBdHV10dHRQV9fHy+++CJ9fX10dHTQ1dWVd2hm41a9A1m2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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb0578feb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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nYTX5e7F+aW9vr7usFtRXrre3dw1rs25pVDDuC3yE1C36W2A34BRJiyKie012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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb087d52b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LwINum5lZoTkRmplZoTkRmplZoTkRmplZoTkRmplZoTkRmplZoTkRmplZoTkR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\nJ0IzMyu0/wOo0rA59dSBhQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb054d8fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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B7f2lU3mDE1XV9fRcM6sNz88BPwVWAO9sn9oHeH1VfbDn5R/r+Xkf4IyqOq5n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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb0565c6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ToZmZFZoX5jXrJ1UfsXtD9erb9k2bVq0us4HGidCsH1T7sZoR0xZVvU6zonLX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\nRGhmZoXmRGhmZoXmRGhmZoX2/wFzmchN4Efb1QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb087d53c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xc+DnAJLmb8D5n42Ip/oRl5mZ2aAY6M4yP5E0AngYuCAiflyqkKTpwHSAuro6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb0bd01d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KWFPysWGN+Lj4ux0j4lX9bVR66NnfSbolIiaVXQ9rPj42rBEfF4Pn7k0zM6sM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\nMzOrjP8P0dgQ7CyMgx4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb05546240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb05e1dc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Dp+zVcFozK6fzzz+fkSNHsuuuuzJy5EjOP//8VhdpUKlbI6zhDOA2YHYPaTqB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\n5EdSjTOQvEcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb0bad99b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JGlxI2xXoD9xcOxARs4AZwG750EigA7in8L67gTcKeczMzFquqZZnE6YC1wAzgeHA6cBv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\nnMKixAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb08d5e828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for c in df.columns[1:]:\n",
    "    df.boxplot(c,by='Class',figsize=(7,4),fontsize=14)\n",
    "    plt.title(\"{}\\n\".format(c),fontsize=16)\n",
    "    plt.xlabel(\"Wine Class\", fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**It can be seen that some features classify the wine labels pretty clearly.** For example, Alcalinity, Total Phenols, or Flavonoids produce boxplots with well-separated medians, which are clearly indicative of wine classes.\n",
    "\n",
    "Below is an example of class seperation using two variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1fb0968b748>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BU0oppZQKMk3AlFJKKaWCTBMwpZRSSqkg0wRMKaWUUirINAFTSimllAoyTcCU\nUkoppYJMEzCllFJKqSDTBEwppZRSKsg0AVNKKaWUCjJNwJRSSimlgkwTMKWUUkqpINMETCmllFIq\nyDQBU0oppZQKMk3AlFJKKaWCTBMwpZRSSqkg0wRMKaWUUirINAFTSimllAoyTcCUUkoppYJMEzCl\nlFJKqSDTBEwppZRSKsg0AVNKKaWUCjJNwJRSSimlgkwTMKWUUkqpINMETCmllFIqyDQBU0oppZQK\nMk3AlFJKKaWCTBMwpZRSSqkg0wRMKaWUUirINAFTSimllAoyTcCUUkoppYJMEzCllFJKqSDTBEwp\npZRSKsg0AVNKKaWUCjJNwJRSSimlgkwTMKWUUkqpINMETCmllFIqyDQBU0oppZQKMk3AlFJKKaWC\nTBMwpZRSSqkg0wRMKaWUUirI6iQBExGniCwRkRl1sX+llFJKqboUUkf7vRFYDcTW0f6VUqrOZGRk\n8Pnnn7Nx/SaioqMYMLA/PXv2RETqOjSlVJAEPQETkVTgHOBR4JZg718ppeqKx+PhqSeeYuqb7xLv\nSSLSRFPqKWXa6/8jJS2ZFye+QMuWLes6TKVUEIgxJrg7FPkQeAyIAW4zxpzrp8xYYCxASkpKj2nT\npgU1xvpu3759REdH13UYxwyt7+D7q9b5ju07yM7MIdIZhfj0AClxF1PmLKHV8a1wuVxBjeuvWt/1\nldZ38AWzzgcMGLDIGNOzqnJBbQETkXOB3caYRSLSP1A5Y8yrwKsAPXv2NP37Byx6TEpPT0frJHi0\nvoPvr1jn69ev54Yrb+Kk2IG4nP4TrNUZv9F7eHf+/fijQY3tr1jf9ZnWd/DVxzoPdif8U4AhIrIJ\nmAYMFJGpQY5BKaWC7r133iPZNAmYfAG0jGvDjE9mkpeXF8TIlFJ1IagJmDHmbmNMqjEmDbgE+M4Y\nMzKYMSilVF1YvnQFCWFJlZYJCwknQiLYsmVLkKJSStUVfQ6YUkoFQUhICB7jqbKc23gICamrAepK\nqWCpswTMGJPurwO+Ukr9FZ024FT2lu6stExecS4SDmlpacEJSilVZ7QFTCmlguCiYReR7dzLvhL/\n/buMMazft5pLR/2D0NDQIEenlAo2TcCUUioIkpKSuP+Re1m272f2FOzC+xFAxWXFrMxaTHL7eK66\n+qo6jFIpFSza0UAppYJk2PBhxMTG8NS/J7Bx52oiJRo3bvLI5txh53D3vXcRFRVV12EqpYJAEzCl\nlKpFhYXAMy2UAAAgAElEQVSFzJs3j+zsbOLj4+nTpw8RERH715911lmcccYZLF26lK1btxIeHk6v\nXr2Ij4+vw6iVUsGmCZhSStUCt9vN8y+9xKR33sGRkowjJgZPXh6ee+/liksv5fprr8XpdALgcDjo\n3r073bt3r+Ooj17r16/nvXfeY8mCpYgIvfv25uJLhpOamlrXoSlVLZqAKaXUYfJ4PNx61118u3oV\nTS4fSXjCgdasoqxsXpvxBZu3bGHC44/jcGjX28Ph8Xh47NHHeP+tD0j2NCExvCEYw4xVXzNl4hSu\nu/U6xl59lU5sruo9/U2glFKHKT09nW8WLyLtkmEVki+A8IR40i4ZxlcLFzBnzpw6ivCv44XnX+Tj\nNz+jV0x/2iaeQHJkCslRjWif0IUeUX15+amJvD/t/boOU6kqaQuYUkrVQEFBATNnzuSnH+biLnPT\nqUtHvv3pR2J69cQR4AGqTpeL6BN7MOmdqfVuPrqjSW5uLq+//AY9Yk8j1Bl20PoIVyQdI3vwzJPP\ncuFFFwZ9UnOlakITMKWUqqZvvvmGO266i4iSGBJIwiEOln2zioVZSznh7jsq/WyD9u349bkXq70v\nYwzLly9nzZo1iAgnnHAC7dq1O9xDOKp9/fXXxLjjiXBFBiwTF54AuU7mzZtHv379ghidUjWjCZhS\nSlXD3LlzufWft9Mp4kTi4xP3L081aSzPXk1mRhbOMBfJDRv6/bw4nRWe/VWZxYsXc/9dD7B9405i\niccA2SaD1h1b8e8nH6Vt27a1cUhHna1bthJWFjj5KhfujmT79u1BiEipQ6cJmFJKVcEYw6Pj/02r\nkI7EhydWWCciJIQ1wOzOZk+Ig8QGDfaPdvSWs2Ejbdu0qXJfCxcu5MqRV9HctOPkuA77O5MbY9i8\neiMjLhrJux9OPewkrKSkhG+//Zblv60grUVzZs+eTb9+/er1PJSRUZG4Ka2ynNvhrvDoD6XqI+2E\nr5RSVVixYgU7/txFo+imfte3i2xN/uKlODwOcrKzD1pvPB6yf13AVSMvq3Q/Ho+H22+8g5bSkaax\nzSqM5BMRmse1pFFxGnffds9hHc/MmTM55cRTeeSmx/j61Tnk7M7jnn8+QN+T+zF37tzD2vaR1Ldv\nX7Kceyud1LzUXUq2Zy99+vQJYmRK1ZwmYEopVYXNmzcTI3EBH23QLK4l0bsLyflpHgX78ius85SV\nsWXml3RIaMCZZ55Z6X7mz59P3p4CUqKaBCzTLLYF61dvYM2aNTU/EOCLL77grhvupbWnC93i+tC2\nQUfCQyLoEXcqTQtbc+3/Xcf8+fMPadtHWrt27WjfpS0bctb6XW+M4feclQw8awANA9wKVqq+0ARM\nKaWq4HK58EjgVhenw8mARgMJXb2VbW+8yeYvv2Lr3Hls/vIr/nj+JU5JTuHNiROrnGR7yZIlRJfE\nV/oMKxEhjgb89ttvNT6O0tJSxt/7MJ0ieh50KxUgOTKFVs5OPHD3+Gr3Vwu2Z194huLkXFZmLKag\n9ECym1ecy2+ZC4hsGcIjjz5chxEqVT3192a/UkrVE927dyfHnUmpuwSX038S5XKG0ighkbseu529\ne/eyJzOThp2TOPtf/+a4446r1n6qm/SICB5P4IQwkPT0dBz5ISTENQhYJiWqCZu2rmXJkiX18kn9\njRs35qPPPmTiyxP5cNpHOItcGGNwRAgjxl3ClVddSUxMTF2HqVSVNAFTSqkqJCUlMfjsQSz9YhXt\nE7r4LbM9bwtRyRGcf/75h/y0+/bt21MY+l6lZYwx5JF9SJ3w165ZS3hJdKVlRIQYE8/vv/9eLxMw\nsM7Hvfffyy233cK2bdtwOBykpqZW2cJ4tDDGsHTpUmZ/O5vcnDyaNT+O84acR0pKSl2HpmqRJmBK\nKVUN94+/j+HLLmbllsW0imtPeIg1yq7MU8bmnPXsDtvClFcmH9ZUQ/369cMRY8gs3EtiRJLfMjv2\nbSWleTJdu3at8fYdzurFZsTUaCqf4uJiFixYQF5eHklJSfTo0SMoUy5FRERw/PHHH/H9BNPWrVu5\n7upxbF63lQR3Mi4JI13m8uyTz3HBxedz/4P36QNm/yI0AVNKqWpITEzkf9Pf5+mnnubzj2cQJTE4\nxElOaRa9TzuZ5+5+kjbVeMxEZUJCQvjXk49w89W30oEeByVhu/btYKNZzRuPv3ZIcx1269aNN1xT\nMCZwguUxHrJNRrUSvLKyMl584SXeeuNtXCVhuAilmEJC413ccMs4hg0fpnMy1sCePXu45MIRRGcm\ncnLcwAp1V+ou5av3vmVf3j6efnaC1utfgCZgSilVTYmJiTz62KPcefedrF69GrfbTYsWLWjcuHGt\n7WPQoEH855UJ3HfnA2zMESJLYzHGkB+aTUSDMF599hV69ux5SNs+6aSTiGsUw449W2kS479f2ubc\n9bQ7oU2VyaTH4+HGcTex4OsldIw5kejYA/2usvIzeOyep9i+fQc33XzjIcV6LHr9tTdw7g2nZeLB\nt5ddThdd43vz3Rffs3zMcjp37lwHEarapAmYUkrVUGxsLCeddNIR2/7gwYPp/0t/0tPTWblyJU6H\nky5du3DKKacc1q09h8PB0889xf+NGIM7p4zU2LT9LSluj5vNuevZG7mN5556t8ptzZgxg/nfLKBn\nwmk4HRUfPJsQ0YDurj5MemkyZ5x5Oh06dDjkmI8W+/btY8OGDRhjaNGiBbGxsTX6fHFxMf975wO6\nxJwcsIzT4STZ04S3p0zlqaefPNyQVR3TBEwppeqhkJAQBg8ezODBg2t1u926deOt9ycz/r6Hmbf6\nW+IciXRxt2Jezrec0L0jLzz2Hq1atapyO5Mmvknz0NYHJV/lwkLCSTGpvDX5bR5/8rFaPYb6JCMj\ng/8+8xyffvQZ4UQAQqHJ59y//40bb7mx2h3nd+3ahZQ5iIysfJBEUkQKK5etrIXIVV3TBEwppY4x\nnTt35uPPPmTNmjX7J/v+9OuPadmyZbU+X1BQwJpVaxjQ4LxKyzWKTOWnH+rvk/UP1+7duxl+/iWY\nHSH0iDtt/8CM4rIifv5wMT98fyHvfzyN1NTUKrfldDrxGHeV5TzGTYh2wv9L0AexKqXUMapdu3YM\nHTqUuLi4aidfAG63G4fDWWVHcKfDibus6qTiaHXXbXcTsiuSjg267U++wGr9a5/YheisBtxyw63V\n2lbjxo2JSYwhqzCj0nK7i3dwan+dZumvQBMwpZRSNRIVFUV8YjzZRZmVlttbsIu27Q9vZGh9tXnz\nZhb8vIhWce0ClmkR14Y1v61j7Vr/Uyd5czgcjL5yFBsK1gR8IG9BaT4ZsoN/jPjHIcet6g9NwJRS\nStWIw+Fg1BUj+bPgj4BljDHs9Gzh8jGjghhZ8Pz8888kmAYB+8ABOMRBvDuJefPmVWubIy8bSYvu\nx7Es61eKygorrMss3MuSvHncdPeN1Z5ZQdVv2gdMKXXUWrNmDZ9+8inbt+4gsUEC55x3Dj169Diq\nn5Hk8XgoKyur9091H3HpCD6Y9hF/bF9Fq7j2Ferc7XGzMnsxHU5qS9++feswSv9KS0txOp2HNaK0\nuLgYMYGTr3IO46SoqKha2wwLC+PNtyfx1BNP8dH704k2sThMCIUmn6gG4Tz0rwcYOnToIces6hdN\nwJRSR528vDxuuv5mFvy0iCTTiAhnNCXuP/j03Rmktm7CK6+/TJMmTeo6zBqZP38+k157kznfz8Hj\nMTRIasBl/3cpl/zjEhITD544u67Fxsby3gfvcO3Y65i/cjYJ7oaEOSIoNPlkyE76n9GXJ55+Aqez\n6iQlGPLz8/noo4+Y8vpbbNm8FQS69+jGFWP/j8GDB9c4GUtNTaXImV9lueLQApo1a1bt7UZERPDA\n+Ae4+dab+fXXXykoKKBRo0ZBm11ABY8mYEqpo0ppaSlXjr6KHUsz6JMwGIcc+FI63nRg/e9ruXT4\nSKbP+Jj4+Pg6jLR6jDE88/QzvPXKVBpLGn0TzsYpIeQWZzPtPx/xzpR3mfr+27Ro0aKuQz1Iw4YN\n+WD6/1i+fDlffjGL7MxsGjVtxJAh59WreDMyMrjsklFkbcijWXgr2iR1x2DYvnwLd197H7PO+YoJ\nzzxVowTntNNOgyg3OUVZxIUn+C2zrySPIlc+gwYNqnHMMTExh/Q5dfTQdFopdVT5/vvv2bDsTzom\ndKuQfIE1kfTx8e0o3QHT3ptWRxHWzBdffMFbL79Dz9i+tIhvTYjDhYgQF55Ap8SeJGQ34opRV1Ja\nWlrXofolInTu3Jk777qDx578NzfeeEO9Sr4Abrj2Roo2euiW2JsGkQ0RERziIDW2OT3j+vLjjJ95\n+aWXa7RNl8vF7ffcxoqChRSUHtwSVlRWyPK8X7npjhsIDw+vrUNRfyGagCmljiqTX59CY2fzSvt5\nNYtsxVuTpgYcTVZfGGN46b8v0yq0A6HOML9lmsW1omBXEenp6cEN7i9i1apVrFy8irbxJ/hd73Q4\naRfVhcmvTaGkpKRG275o2EXcfP8NLCr4kRVZi9iet4XteVtYmbWYBft+YOxtYxg16q85CEEdPr0F\nqZQ6qvyxbj0dIiqfCzE+PJHsjCwKCgqIiooKUmQ1t3nzZrZu3EafuMqn6kkyjfn4g+mcfvrpQYrs\nyHK73fzwww/MmjmLvNx9NGvRjAsvuuCwJzP358svviTBnVJpwh4TFoszN5QFCxZwyimn1Gj7o0eP\n5pxzzuGjDz/il7m/ADCo1xCGXzy82k/BV8cmTcCUUkcVl8uFp8RTaRmP8eAxHlz1/InhOTk5hIdE\nVjlqM8IVSebeyp+5dbRYt24dY//vGgr2FJHoSSHUGca67zbx3qT3OXVQbyY8M4HIyMha29/ePRmE\nOaq+BegilJycnEPaR3JyMtf88xqu+ec1h/R5dWzSBEwpdVTpO/A0Fnz4G20SOwYssyNvCyd0OaHe\nP8ohMTGRwtJ8PMZzUH82b/kl+zi+UdXT2dR327dvZ+Twy0gpTKNDXFqFda1NR5Z9u4Drr72B1ya9\nWmsj/lIap1DkWVRluWJTSGJiIps3b2bae9P4KX0e7rIyOnbpyMhRl3LCCScc1Y83UfWP9gFTSh1V\nLrt8JLsd2w56UGU5t8fNVvdGrrj6/4IcWc2lpqbSuuPx7MjbWmm5PbKdYZdcVGHZypUree6/z/Gv\nh//F5MmT2bt375EMtVZMfHkiUXkJHBebdtA6hzg4IeFElsxdxsKFC2ttn+eddy6Zjl14TOBW05yi\nLJwxDn777TfOGXQeX772HRGbE4jd0Yiln6xm1IWjuf3WOygrK6u1uJTSBEwpdVTp0KEDY28Yw+Lc\nuWQU7K7Q0T63OJvF2XPpf+5pnHnmmbW2z5KSEn799Vdmz57N0qVL8XgqvwVaEzfccj2bytb4HUkH\n8Hv2Khq1TObUU08FYMeOHQy/4GJG/P0ypj/7BT9M/oU3/vU2A3oP5JGHHqm3SUJhYSGffvgZaTGt\nA5ZxiIOGJpWpU96ptf22atWK3v1PZlXWEr+DMkrdJawuWMpJp57Ii4+/Qs+ovrRP6EKDyIYkRDTg\n+IT2nBQ7gDmfzOORh/5Va3EppbcglVJHnXHXjyP1uFSem/A8f+xeSYQjihJTjCPKcNUdV3DlVWNq\n5RaW2+3mtVdfY9LEN5FCJy4Jo9CTT0xyNDfcOo4LLrjgsPfRr18/bn3wZp58+GkSy1JoHtuCsJAI\nsosy2V76J9Gp4bw+ZQoOh4PMzEz+cdEIQnfH0Cd+cIVbYiXuYma8NYvcnFyefPrJene7bM+ePYjH\nSYQrEmMMeXl55GTn4Ha7CQ0LJTEhgfCICBIiGvD7mt9rdd9PPzuBMZdfycJlP9LEmUZyVApuj5sd\n+VvYabZw0eXnM2vm17SP7EaE6+D+Z05HCF3ie/HxtOlcd/21NGzYsFbjU8cmTcCUUkeloUOHMmTI\nEFasWMHevXuJiYmhW7duhITUzq81j8fDbTffxk8zfqFtdDdiY+MA69ERmdl7efi2R9m+bTvjrh93\nWPtZuHAh8+bMo6ikkD/yVrFs569EREXQvn07brrhOs4999z9ndLfeH0S7h1Ojm/Q/qDthDrD6Bp/\nMt98/h3LRy+nc+fOhxVXbQsNDaXMXUphQSGb/9yMcRtCcCE42Lcvn+yMbKJioohMCqv1vnvR0dFM\nnfY23377LZNfm8KitXNwOp30Ob03j465n7KyMj6dOoPEuKSA23A5Q0nwJDFjxgyuuOKKWo1PHZtq\n5TeViMQbY7JrY1tKKVVdDofjiCUas2bNYs7MefRMOK3ChMsiQoPIZHqEnsprz73BwEED6dCh8sdI\nBPLWW2/x9CPP0IQWDEw+l5AUF8VlRfyZu549e7fRqFGj/clXSUkJ06a+T8eYEwNuz+kIIdnThLen\nTOWpp588pJiOlJSUFOIbxLH8t2U0oCEu54Eky4ULiKAwr4ANRau55uraT3BcLhdnn302Z5999kHr\nPvvsMyIkuspthBPNlj+31Hps6thUozZ6EfmniNzh9b6riGwFMkRkkYgc/cN0lFIKeP2VSRznalUh\n+fIWFhJOsqcpb0+ZekjbX7x4MRMeeYZuUafsfwJ++XbbJHakfUh3brzmZtatW8fUqVO547Y72bt9\nL5RUfmsxKTKFFctWHlJMR5KIkNSoATvLNuN0BPjb32HYXryZlq1aBjW2yMhI3FQ900Cpp5iY2Jgg\nRKSOBTVtAbseeM7r/XPAduA24E7gcWBk7YSmlFJ1o6ioiFXLVzGgwbmVlmscdRw/fv/TIe3jjYlv\n0MSkEeny/6DYxIgkzKYQBpw6iBaxrXGWusjPKWBL/lYcIUKz5s2IiIg46HPGGBz1rP8XWJ3w/1iz\ngZjYWNbuW0pzZxtKTBFbndvIcmRSRhnG4aZhaBIzPpnBeeedF7TYevXqRR7ZFJUVEh5ycJ2CVa/Z\nIXsZNLji/IyZmZksWbKE0tJS0tLSaNeuXTBCrnXbtm1j5UorcW/Xrl2NJhBXh6amCVgzYC2AiCQD\npwCDjDHpIlICvFDL8SmlVNCVlZXhcEiVHdmdDuchzdFYUlLCd9+mc2rcgZGape4SSj2lhDpDCXG4\n2L1rN2E5UThCQ+jc/ESMMazfuxZj3ISURbBpwyZatmpJWHjFKYx2FW1jcL++NY7pSNuzZw8huDil\nxQBW7l7Kwj0/UZYQScyJPYlLa4bTFYpk5pK/7Demf/Ul/87IoEGDBkGJLTY2lqHDhjL7vTl0TjjR\n73nfmLOO5m2O23/LOzMzk38/8m++mvkNsY4EHDjJc2eR1qY59zx4N7169TrkeAoKCsjLyyMmJqZW\nH0rrz6ZNm3jkwX/x69wFxIUkgoEcdybdenXlgYfv5/jjjz+i+z+W1TQBKwbKb9wPAAqAH+33mUB8\nLcWllFJH1NatW5kzZw75+fmkpKQwaNCg/dMWRUVFEZcQT05RFnHhCQG3kVGwh9bda/4FVVRUhAMH\nLqeLnfu2sSpvDbtL9uAIDcWUlNDE1YjwvRHEhSTi9rgB6xZe6+T2bNmxkbYhXfC4PezcuZPmac0P\nbLeskAzZyaUjR9Q4piMtLCyMMncpghARGkVYs1SaDjkPR1goDnFat3qjGhDRpClZy37l6htu4IOp\nU4M2mvOue+5k7eq1LFnyMy2i2pIQbiV/+SX72JS3DndyMa9PfBcRISsri4svuITSLcJJcQP2z+Np\njGHH+i1cOXIsz7/2X/r161ejGBYvXsyrL73Kj+k/EeIIpcxTQv9B/Rh77Vi6dOlS68e8YcMGLrng\nHyTsS6FP3OD9t4bdHjd//rqei8//B+9+OJW2bdvW+r5VzZ8D9itwnYh0BG4AZhlj3Pa6lli3I5VS\nqt7Kysrimiuv4ez+5/DK/W8w9dEPePy2pzml56m88PwLeDweRIRRV4zkz4I/Am7HGMMOz5+MvvLy\nGscQFRWF0+Vg+Z7F/FiwkJK+nUgdexWpY8bQ5IoryOrRjLXR69lZtrXCYxFaN+iAIxLWu1chDgf7\n8vIps1vgsosyWZw7l2tuGktaWlqNYzrSGjZsSOPjGrEnfycr962iwcCBhEVG43KGVuhnV2bKaDZ4\nAKu3bmHZsmVBiy8yMpIp70xmzN2j2BKxlnk53zI/9zt+K5vP2VcOYvqMj0hNtbo5T3hiAqVboENi\n1wqTqIsITWKa0SG0B7eMu5XCQv8PC/bnww8+ZPTFY9iUvotT4s7glLjT6RN7Butnb+eyiy7nk08+\nqe1D5s5b7yIpvymtEtpX6JfndDhpmdCGJiUtuOWG2+r9pPZHq5q2gN0KfA4sB7YA3kNVLgbm1lJc\nSilV6/Ly8rh0+EgKN7or/MUPUFCaz5vPvk12Vjb3PXAfIy4dwf/e+4D1O1fTMq5dhZYYj/GwKmsx\nrbu3pH///jWOw+l00uuUE/ngq2857pKRhEQdGIHnDAsjtsMJhDZsxIYP36d7TGeMMYgIIY4Q+rU4\nk6U7fmVZ1lxCTQSFmVlIhAdnrIN777+Li4ZdVMme646IMOaaK3jo1kcpjQ4lLPngZ2m5PW7cUkZi\nYiIlnTow/fPP6dq1a9BiDA8P56qrrmLMmDHs2LEDt9tNSkoKYWEHkqzc3Fw+nz6TE2MDt24lRiQR\nmh3JV199xdChQ6vc7+rVq3n43kfpGtmb6NADnfxdThctE9qQXNyIB+98iE6dOtXaLcG1a9eydvnv\n9IkfHLBMakwa8zfMZtmyZUE9D8eKGrWAGWNWGWNaAclAmjFmndfq2+yXUkrVS1OmvEX2+nzaJ3Q5\naCRepCuK7nF9+N9bH7FmzRri4uJ493/vENHGyS8537MucyV/Zq9nTeZvzMv5lnb9j+e1N1895OeO\n7SsrIbJ3T4gI818gIQpXl7Ysyl7EtI3v8PX2WWzO2YDT4eTE1FM4t/1wohtGcOF15/HMmxP4cf4P\nDBs+rN49gNXbsGHDaNezNWWRLjz7b54ABkrcJRR68mma2oQQl4uwuDh27d1TJ3E6HA6aNm1Ks2bN\nKiRfACtWrCDaEUtYSOUTfMeTxI/p1RugMWXSFFLcTSskX95iwmJJcjc+5BG3/ixatIgEkiqdg1RE\niC1LZPHixbW2X3XAIT0q2hiTYXzaJI0xy40xdfPTopRSVSgrK2PqpKm0jA7cn8XlDKUhTXjnLWsq\nnMaNGzN9xse8/v5E+l9+Mu3+lsbZVw/iw5nv8+obE4mOrvrZUf6UlJSweNlvtB3Ql2IKKSwroMxT\nhsfjodRdwj6TR2kYxPbsieu4Jhz3z3/CoF4sCFnPTzt/wO1xY/AQGhXCtddeS58+fXA6/T8uoz5x\nOBzc/+B9RIc6KHYUke/Oo8Cdzz53Lo5waN6iGXHxVlfikpxcGjYI/GDUulJWVoZU46vTKSGUlVZv\nWqgvZsziuNjKH72RGtWCmZ/OrNb2qqOsrAwxVSfrguOQBpqoqlX5p5uITKrJBo0x+ohgpVS9s3v3\nbor2FRMbV/lYoeTwxiz89cBf/CJC9+7d6d69e63FUlRUhIQ4iU1MJDI2luysLLIysylxuykzZYTE\nREJEBMZViKe0FIczhOgWrYhqnsbuWbNYumcR4c4Qhlx8HjExR9dzqbp06cJxCQmERkfjSmqAx+Mh\nxOWq8PR7YwxFK1dx/pVj6zBS/1q1akVuWTZujzvgM+IAcj2ZdOwc+PZeOWMMRYWFhEVV3qIWHhJO\nQW71+5RVpVWrVuQ7cqssVxSaX6cjIYuKipg9ezabNm0iPDyck08+mQ4dOtTrlt7qqk7b+Qk+75th\n3YLcbb8a2q89wJ+1Gp1SStWBI/2rPSoqCpc4KM7NJSw2lqTkZJKSkyktLWXdH78TlpCAx+MhL3Mr\nzshIMFZQ4nCS2L8/q958nZ7t2nPL7bcc4Uhrn8PhYNyYK3nk9VdJGzmCkKiDn4O2/Ycfadu4Sb3s\nd9S0aVN6nNSNzfM30CLB/8TixWVFZDn2cP4F51e5PREhJjaWjdm/ExMaS0JEEiF+HlSbW5xDcnLy\nYcdfrnfv3kQ0CGNv3m6SIv3PbZldlAlRbvr2Df5jTYwxvP322zzzxH8JL40irCQSI26ec75Iy/Yt\neOb5p+vlYJOaqDIBM8bsn/dCRM4DngXON8bM81p+CjAF0KnilVL1UkpKCuHRYeQWZxMbFrgVbE/R\nDvqc3POIxuJ0Orno73/ns4WLSR3Yf//y3NxcJCwcRHA4nRSvWk102+PJ9+TiIAQwuMPKiO1wPFdf\nO5aEhMCPyKjPLrn4YtZv3Mi7k6YQdWIPkk/ohMPlIm/zFrIWLKJRaRkTJ00KSiuHMYYFCxYw8/OZ\nZGfl0CS1MUPPH1rpoxfuvPcORlw4koh9kTSKblphXVFZIUtz53Pl9WOqTJiWL1/OU49NYM+OPezM\n2YPLGUoRBbRs0JqODbvhcrr2l91WtJFLx11S5fEUFhYya9YsfvzlF9xuN53bt+f8oUNJTEysUM7h\ncPDgow9w8zW30cnRk/jwiutzi7NZWbiQRx97BJfLRbBNemMSzz/2Ep2jexEdGbt/uTGGTWt+55IL\nR/DRZx/QtGnTSrZSv9W0D9jjwH3eyReAMWYu8ADwRG0FppRStcnpdHLZFZexYd/agMPqS9zF7Jbt\nXHrZkX+O1hWjRlG2YiXZ6zfsX+YuKwO7L9e+ZcthbwZd/nYWLVq1oNFxKTRu1pi27drSsEUabrc7\nwJbrPxHh3rvu4o0nnqRrcSkb/vsiax6fQMjc+dx50TA+ef/9Wm3tCWTbtm2cd/YQ/jlyHPPeXcz6\nr7fx1WvpDDvnEq78v6vIy8vz+7n27dsz6Z3X2R37JwtzfmRdxio2ZK1jedZCFhb8wBU3jeKGG6+v\ndN/z58/nsmGj2LtgH6c3HkobV2fa0pVOciJ792SQvmEWpW6r79XW3D8piS1g2PBhlW5z9uzZ9B44\nkPFTJvNTWQnzHYbnv/2GU888k1deffWg637QoEE8+fxjrGUJS3J+Zn3mGtZnrWVpznxWuhfy0IQH\nOcjGJFYAACAASURBVPfcymeDOBL27t3Ls08+R7eYPkSHxlZYJyK0iG9DVFY8Tz/5n6DHVptqOnyn\nJdbDV/0pANIOKxqllDqCLh89ii8++4LVG5bRJq5ThVs9BaX7WJ63kEuuGB6UB082a9aMSc89zxXj\nriMjtSnxXTrjBgq3bCFnw0bIyKTrFZcTEh5OCBDuNe2Qycs7alu/yokIvXv3pnfv3gD7H7VRm/bs\n2cNHH37E7K++o6SkhLYd2nLpZSPo3Lkze/bs4ewz/kbOln2EiIsCZzHNE1rSOPI4GpHK6vTfGXvF\n1bz93lt+R7p269aNH+al88MPP/DTnJ8oLiqmTfs2DBkypMpzY4zh+qtvoI2zC0kxKQC0aJHGpo1/\ngkdIk7ZsLFjN/K0/EBsXg4kvZcrUyQe1YnmbN28e4+69l0bDLiCmaROvQLtSnJvHf997F6fTyVVj\nxlT43FlnnUX//v35+uuvWfjrIgC6dOvM2WeffcSfwh/Ixx99TIInucIz8Hy1iG/DN19+S+aDmZXW\nS31W0wRsMTBeRH41xuwoXygiTYDxwKJajE0ppWpVdHQ07/xvKvfceS9zZn9DAsk43E5KXUUUuvYx\n9taruPqaq4MSy+LFi3nxtdcoLC6mcNVqtvw8H6fDSWFhAU3/djYp551DuJ8vluLcXNzbd9T4Kev1\nXW0nX59++ikP3Pkg8e5kkl2NCZcolq5dzTefjqFr787MnzefnM35pDpaEi4R7Czbws/ZP2AwRLti\ncEsZG79Zz3vvvcdll13mdx9Op5OBAwcycODACstzc3OZNWsWWzZvISIygn79+tGxY8cK60MKwkmK\nT9m/LDwigjZtW5Odk0NWRhYppU1ZU7SE2ydM4IILLqh0xK0xhvGPP06Dv51RMfmyhcXG0OziYTw7\ncSKXDB9+0MCN8PBwhgwZwpAhQ6pVt0faol8XE++sfARsqDOMaGcsf/zxx2FN+/T/7J13eBRVF4ff\n2b6bZNNIDy0h9N6bICIiwidgo4igNDuW77P3rqjYBZEmEOnSURQElCZSQ28JBNJ7Npvtc78/goGQ\nAqElyLzPk4dk7507ZyZD9uy55/xOVVJZB2ws8CtwQpKkHZxNwm8DZKE04lZQUKjm+Pn58e1335Cc\nnMwff/xBYWEhoaGh3HzzzdfsE/+y5ct54f33MN/UhfrPPoVHCBJPnCTvyDEcf2wkbdNfqCPrkJ6R\nRVBwjaLtOElCdrtJWr6KEfcNKm6bpFCaP//8k9f++yYtTB3x0fsWvx5oCqa2px6/LViO1Wmlrb4b\nKknFIeduHB47jaQ2GIUXLrcDo96LlMKTPPXIM/ww9QdysvLQ6bTcfOvNPDBiGI0bNy51XlmW+fKL\nr5g2aRo+Hn8MHi/cwsV3E6YQ0ySaL779nIiICPLz8gmgdOK7Sq0mICCgOKLjshTQtGnTC8qd7N27\nl6TcXKJiyi4KAND7+aKpXZNVq1YxaNCgi72VVUKRM35x6vvXczVkpRwwIcR+SZKiKVLAbweEUtSc\nezYwXQhRYY2sJEkG4A9Af+bcC4UQb1yK4QoKCgqXQ3h4OIMHXzip+Upz8uRJXnr3XSKGDcEUVAO3\ny0X88XjUbg1BUc3wC4vmxNwfyJyzAL+uXUl3uHAVFqLOyaXg7x30bNWaZ8aNu+Z2VxWyLGO1WjEa\njRcleiuE4OMPPiFK06iE8/UPBfkF1JEbESe24sBGtjsDp8dBQ6l1kSipVNTpwONx4y8Ho7Zp2bN1\nH30a3IXkhr8XxbHyp/t54n+PMvbhkjIZH37wEYumLaGtuTsGzTlbxkKQcOAIgwYO5qcVi5CFKCUE\nXBZqSY3T6bzgvBMnTqCPCLugM6IJC+Xw8eMXXK+q6dilA1M3zCSygqwmh9uOVbZc130qKy3hLISw\nA99e4vkcwC1CiAJJkrTARkmSfhZCbL3E9RQUFBSuK2LnzkXXtDGmoKItlvS0dFRudbGyutZkIrhz\nd+T1f6P+fQdZjixSZBt9br+NJ19/g27duqFSXZKG9nVFfHw806dMZ+lPy4oETSXo1acXo8aMpHnz\n5uUed+zYMU4ePUVn37I1uLIys9CrDAQRTqr7FFmeNKKlZiUU4bXosLry0aEnSArDSi4Z1lTq+sdQ\nX9eEWu4ovvloEpE1I7njjjuK7Z07fR7tfW8u0R8SiqI0UX4NOJC5i2+/nkijJg2xeHKB2pSHR/Zg\nceVRs2bNC94rrVaLcF9Y9FV2e9BXQUVjZRkwcAATPvycAqel3O4A8XmHueOePpjN5jLHrweu6f9i\nUUTBmR+1Z76ULp8KCgrXJUIItm3bxlNPPE2fW/vSv88AvvziS1JTU8s9ZuVvvxHQvEheUfZ4yM3N\nK/WG7VMvhnyPhZ5hvRhcdyhtfFsSdaY1zo3Axo0buavvPWyZv5O2xu7cHNCPLubbOPRzAsPuHsHC\nBQs5cOAAL732Gr0HDKDP3XfxzvvvEx8fT0pKCt4ac7nRIJfThVqlwUvyweLJAyHhLZ1XaYcEAjTo\nUKvVBEqhnMo9UTxu0BiJMTTly0+/Lq4snBM7h0ARVup3eS51zQ1YvGAJvr6+ZJKCWy5fYf5UfgKt\n2re8KJmF1q1bYz+RiNvhqHCe++gxOnfseMH1qho/Pz9efftldhdsIceWVWLMI3s4mrMfT4iNZ//3\nTBVZeGWQLtTlXJKkdKC3EGKXJEkZXMBhEkKUreh2dj01Rcn69YBvhBAvlDFnLEX5ZoSEhLSZO3du\nhTbeaBQUFFxyCxSFyqPc72vP9XDPZVnmVOIpCgsK0aBDo9IghMAlXHgkF+ER4fj5ldYbO3j4MJrA\nACS1GiHLOBxOVGV8FnZmZGDWmnG4bDg9DiRJhVanQaVWEVgjkMDAwCuW/1Jd7rcsy2RnZ5OclIwG\nHXqNHq1KV2KOR3jId+Wh1mlQe3mh1heNe+wOZJsNX29vCnILMKnLjpzY7XYkJNzChUsUbe8ZKZlP\nJxDIyKhQoVKp8Ag3bpWr1Jam1ZNPVEwUer2e+OPxYFehUVUcYSqULYTXDKfAUkB+jgWj2qvI4TsH\nt+zCjo26UXUwnlP9WhGJp05hlWW05rKv22Ozg9VKgwryxKobeXl5pCSngkcgoQYEHtyYvL2IjIyo\nVB/Wa/mM9+jRY4cQ4oJighdj/TdA2jnfX1bESgjhAVpKkuQHLJYkqakQYt95cyYDkwHatm0rbr75\n5ss55b+O9evXo9yTa4dyv68918M9f/yRx9n1236a+7cr1dDY4shnt3Uy3874iptuuqnE2KfffENu\ni6b414vGbrORcPwEXuc5Cy5LPikzZ6GzCkLlWgRKIei8tNSNqkuOPYv4woM06hTD5GmTS7TwuVSq\nw/2e8+Mcxr/3MY50D1KuFq1KS46Uiaxx07FWN4K8QgHYnbGDw96ZRA4eSG3/aBBntt70apwuiZNT\np2CLP0U3v95lbl+lJKdgySrgGPsI0odw3HKYVtxUoq2QQ7bjxoWPzoxGoyHJfQKVn6BDzZK/y90F\nW/hk6od07tyZiV9Own1QR4h3WJnXl23L5Ej+YY4UHuHDt99k2erVeEtqDscdJViKwKzxwy27ySYd\nl8nOV5O+KJbouBgyMjK4+/6hWGpGEtqlM1pTkeMmu92k7dqNY/NfxE6eTLNm5ze3qd54PB42bdrE\nqVOn0Gq1dOzY8aIjwbIss3v3brKzs1GpVHTp0qVKRGXL42KU8N865/s3r9SJhRC5kiStA24H9l1o\nvoKCgkJ14ciRI/y5ZjOd/W8t5XwB+OjNRDsb8+lHE0o5YMPvu493f4zFv140er0eJIEsyyXyuvL2\n7UW22oiiFQHaYGzuwuJP7/6GQFrru7BryxYmfTuJcU9ffwn5DocDq9WKt7c3Op2OH2N/5KPXPqGF\nT0eS7SlotXrUKjWRRJHtyeDPhLV0j74Nb62Zw4XHCL33AQpsdhACzokC6ry9iLirP0e+nsQhSxxt\nAjqXihIGBgYQn3EUp9ZOm5iOZB/MIMuWQg1R5DgJBC4c6NR6NJqiqGYGyXQOLC374ZTtxTlInbt1\n4qe4lYRQ2gE7lL2POMcRjK1bEBTdBn1IMPYObUndvhPfOkHc1KU9qUlp6PV6xt7+AL1798ZgqLg3\n5PkEBQXx049z+PDTT1k1cTL6sFAkjRpbUjLtW7Tk5RkzrsuEdbVaXelWSEIIFsxfwFeffYMt245B\nZWLYk4Po2v4mRj0yitFjRlWLPMpKJ+EDSJKko6hHZACQDewVQlywVEOSpCDAdcb5MgK9UNTzFRQU\nrjMWLlhEkAgr0/n6hzDvSLYcXsPx48eJjo4ufr1v3758M3UqKVu2EtapI/4B/uRl5mNUFW2DFZxM\nwLpzNz6yLwHa4KKKPMldQtxTkiRivJoya/psHnnskSsSBbsWxMXFMXn6dNZsWI+k1SJcbnp07crv\nK36lo88teOl88HhOozvnvgaog3C767E76W9qB0Shr1cXrckLuzsPWQhU5zlYpqAg/OpF4e+Q2RG/\niWhTI/yNgUBR5dwJ6zFs4Tl4yyZO5SXQslY7NiWsw1f4o8OACyeB/oEU5BUghCDecxCzl5lAY8ns\nmmxbJqYAU7EcxX2D7mPKN9ModFkxac9uaZ7OP0mcHE/o4EG49BJ+QX5IKhV+UXXxi6pLysZNbIvb\nw6rFiy/bKahRowaffPABrzz/PPv370eWZaKiooiMjLysda83JnwygdhJc6lvbE6Ab1Gxi0nlQ4yn\nBd+Pn8bRI0f46OOPqtwJq/TZJUl6nqItyW3AauBvIE2SpOcu4vAwYJ0kSXFnjvtNCLGisjYoKCgo\nVCWJCSfx0lRcfSVJEl4an1IJ+SaTidipUzEfjefErB8hLR1XXhbZ8YdIW7mCglVrCBX+hEiReGQP\nhZ4CQsNC0GhLfl720ZuR7Br27bs+NhCWLlvG4LFj+Uu4iRr3ODHPjCNq3GOst+aTXGghozAdAI1G\ngyxKtlmqoQ4j35ZLlj0TTVAgspCRJKmU8/UP6sAAho0YxqOvjua091G25K1hm2U9220b6HhvS9b8\n8SuzF84kqIMPh1178A3yZpfYxAnNIUwhOrxqGMmW0tjh+hO8PHSu3aNEJM3lcXHUto9Hnhhb/CYe\nFhbGMy89xW7LFnLsZxPH91r249f9Jtx6FWq9iqCgkgKjYV27kGQrZNOmTVfkPgP4+/vTtWtXunXr\ndsM5X3v27GHmd7Np7duFAGPJe23W+9HarzNrl6xnzZo1VWThWSoVAZMk6WngA2ASMI8iRywEGAR8\nIEmSQwjxZXnHCyHigFaXbq6CgoJC1eNj9sHpSbvgPJfsLDOJOiIigl+WLmXdunXELlpIUkoKp04k\nQkYeEebanE4/iV72xqGxlZvMD6BRabDb7Zd9PVebI0eO8NL77xM+bDCmGmffFDUGA16NGxFs8GXb\n4hX4GwIICAwgMyWrRJsolaTCR/LD5XYi2+w4PQ78A/1KbD+ei7A7MZvN9O/fnxEPjuDUqVO4XC5C\nQ0OLt3Jr1apF+9ntycrKIjs7G7fbzeZNm/l5+S9Y7Rm0adOUXTtdmKy+FLqs6NR6PLKHJEsiSXI8\ndw7ty5ChQ0qcd+TIkfj6+vLph59xPE9GcqrJJI/giACMvkbCI8JRqdWl7DU0a8KCpUtLbVcrVJ5Z\nM2YRImqWW42qVmmI1EQxbfJ0brvttmtsXUkquwX5OPChEOKVc147DPwhSVIuMA4o1wFTUFBQ+DfQ\np18fNqx4lSjqlzsn35GLZBLlJj1rtVpuu+22Em8C6enpbNmyhfnzFhC/IYmGYQ2hnEJHWchY3RbC\nwspO+q5O/BA7G2OrFiWcr3+QkND5+WNq1YIj+w7TOrAdGekZOD1OdOqzW6sCQaCxBqcPHETftimB\ngWUnYrvtdhwJCXTp0gUAlUpF7drl620FBhZVlEJRk+1Ro8/2SszJyWHe3HnMnDab7MwsBIL2Hdrz\n7Njx9OjRo8wq1Lvvvpv+/fuzdetWNm/eTNaypdRv2ABNBcnfBn9/Uo/GlzuucPH8uX4jjXzaVDgn\n3KcWv29fhtvtrlQl5ZWmsmeuCawrZ2w98N/LskZBQUHhOqBbt24Ya+g4nXWSSHPpN3dZyBy17mPE\ns8MrVXUVHBxM//79adq0KQN6341HeFBLpSMmAMmWU9RvEkPdunVJT09nwfyFbNu8DSELWrdvxX2D\n7yM8vHRfwIvBarVisVgwm81XpD3Tsl9+IXzUg2WOeXl7kZeTj0/DRpz8ew7t1B2pE1WHEwkn8Hjc\naCUdAplcOZMaBCC5bBhTktE1b1pqLSEEyWvX0afHLdQow9mrDElJScydP58de/cS1aIhg1q04L57\n7rkoh1ej0dC1a1ciIiKYsWQJ6jKiXufiyMujRsD13Vy9uuB2u1FpKr7fEhKSpMLj8VSpA1bZHLBE\noLyYXa8z4woKCgr/ajQaDd/PmEyKMYFD2XHY3UVd2IQQZBamsSNnI616NCvVquZiiY6OplffW4jL\n3YZH9pQaz7PncEI+xH9ffJbp06fTs2sv5n++mPydLgr2eFj8zSp6d+/DV198xYW0Hs9l586dPDL6\nEdq36EDvbnfQrnkHHh3zKLt27bqk64Cie1JoLURXjgaTj9kMKoHQa3F5imq5DAYD9evHUCMsEFnr\n4qTnGEZ/Pff/bxB//P4bNVLSObl8Jbass7lW1tQ0TixaTE2bnbdee+2y7J3wxRf0HDiA2XG7SKwT\nSUJkGNP/2sItd97JzNmzL3qtOnXqUCs4mNz4iqNbtn37uec/1aMR9vVOvZh6ZJ3JJyyPHHsWwSHB\nRVXIVUhlXb8vgS8lSQoAFlKUAxYM3As8CDx1Ra1TUFBQqKbUr1+fJSt/YvKkySxduAyVrMEtuwgK\nC+KZR55k0KBBF4x8VMQH4z/gf67n+PO3dQSLcHz1gbjcTk7kHuOUNYHQ8FCeeORJcpLz6BpyK16G\ns5pXoURgd9uY/uVMTF6mEttq5bFwwULeefk9wqlLF9/b0Ki0uDwuEtYlMGL9Q7w1/g0GDhxY6euQ\nJInAGoHYMjMxBZfW6ZYkichaNTm+czdqlRohRFGCvVqNn78v2ao0AgO8+H3JyuKI3pK5c5k6fTqz\nf5yPSyUhhMBbo+XRwYN5cPjwy4raTZ4yhSnLl1L34dFoTSYsFgtZWdk4oqPxhIby/IcfYLPZeHjM\nmIu69ifHjOF/H4/HOzwcbRl2pW3fQRCqSkstKJTNiNHDeWPcO4SLWuUKFSfajjP6mRHX2LLSXFAJ\nv9QBkjQGeAMIp0iUVQKSgTeFEFOutIFt27YV27dvv9LLXtdUB9HEGwnlfl97rrd7brPZyMjIQKvV\nEhoaesUU6oUQ7Nu3jx9n/cj2bTuJ2x2HWedHY/8WmPW+rD6yjGjRBKPGizp162AwltSOsjotxLm3\nsunvjaWckoKCAlasWMHuHXto1LQRb7/0Dp0Db8XHULq60+LIJ86+lYUr5xNzCUrqn3/xBT/s3E7N\nPr3LnXP0pyVo9h9B49RhVvkhI5MrZ9Gxawfeeu/NMrdTnU4naWlpqFQqQkNDL8vhhaKt1449byH8\noeFovb05ceIkDpsDLTo0kgaBwJqRQvrCBXz76ScMHzH8gmsKIfj8q6/4fsF8vNu3pUbzZtzl48+P\nJ4+TtW07XukZzJk2vcI8NYWLx+l0MmzwA6TuyaKxf6tiqZiOI5uzZeoejuUdhAgHi5YtvGp9JCVJ\nuigl/ErLUAghvqcoF6w20OnMvzWvhvOloKCgcD1gNBqpVasWYWFhV8z5gqIISrNmzXjmf8+Qm5tL\np9Ae9Kp9JxHm2uQ78vHCTKA2BK2sIyEhAfd5DZm9dD4YnN6lSu7nz5tPl3Y38dVr37Fn8WEsORb0\nmT6cPp5Efn5+KTt89GaC5HBm/XDx22/nMnTIEKTjCWQfPlLmeNbBQ5iSU1m7bg0zf5rOs+Of5IVP\nn+WX9av4fvrkcnPZdDodNWvWJCIi4rKdL4DVq1ejighH7+tLYmIirkI3XiofdGo9KpUatUqDOaQm\npqAI3nrpHdauXXvBNSVJ4plx45j+yae0cno4NuFL7Kmp2Ff8wmM9erJy4SLF+bqC6HQ6psz4npiu\ntdmcu4ZD2XGczD2O3WNja95azI31xM6fXS2aeF9S9pkoCpudOvOloKCgoHAVmTtnLqYCM+H+NYtf\ns7osmCjKq9KqdbjdbnKycwgKDipxrN5l4tSps3+qFy1axHsvf0AL7054exdtW3pkD5HaKNRCw+mT\np6lZpyY+PiXb+ER612XF0pW8/e5bVJbg4GBmfPstDz32GIkHD2Fu0RyDry/2vDzyd+9Bk5LKzO++\nIzg4mODg4Cprl3MiMRFVcBA2m43CAhveanOZVai6sFAC8y18Nv5zbrnllotyujt06ECHDh0QQrBh\nwwY2P/bYVbgCBQCz2czUH6Zy+PBhli1dTlpyKuZAb6YvmEqLFi2u6Ieky6HSDpgkSeFAPyASOL9X\ngiirubaCgoKCQuXweDz88ccfHDhwgC8mfEk9TZPi/CgAtaTGw9kEfQ1a0tKKtMkMRgM+3j4ggSx5\nirXIHA4H77/1Ic282hf3SSz6PC3QokNSSRgwkZKUgk/Dkg6YXm2g0FJ4ydfTvHlz1q5YwZIlS5i3\nbCnZOTkE+PszesBABgwYUC0iEiajEdnuJDc7Bw3aciVAhN2Bv6EGp+NPcezYsUpty1aXN/8bgQYN\nGvDc80Xtl9avX0/Lli2r2KKSVFaIdSAwB1AD6cD57YcEoDhgCgoKNzRJSUnMnTOPlUtWUmC1Eh4W\nxv0PDaVv374XlSC+bt06Xn3+NVx5MianGVWygYPqfRxM30v7ml0J9gojxDuCPezA5XHhcXkQAlzC\nTXZaLrLkQVJDeEQYuepMOnfuDMDatWvR2vT4+PqSWpDE0YyDZNsyqS+eJtOZhr+2BhpJg8Ntw2q1\n4uV1tqWOxZlHcBlJ9JXBz8+PBx98kAcffLDUmMfjYcOGDcycNovDBw+jVmvo0q0TDzz4AE2blpac\nuBrc1LUrX86aiYiJLlf+Q3a5sMcnEBpyBxZnNhkZGZeUF6egUNkcsPeBX4EQIUSEEKLueV9RV8FG\nBQWFq4AQAofDgSzLVW3Kv4pffvmFO3r2Y/mk1YTmRdFYtEWV4M1nL39F397/4fTp0xUev27dOp4a\n+wyRhTG09b2JxkEtiNDWpYmqHTXd9diY8DsZ1lS8dT74Gfw56TiGJFRISKglFUaNES+1NzrZwI6E\nbdQID6Bhw4YAHD92HL3Ti82Jv/N3wmYMBd40Em3QSXoyPCkUOCxYXQWohBqnw1HCrtO2BIYOH1yu\n3bIsY7fbKyV78Q+FhYWMHDGK58e+TOa2Ahp4WhPlaMLOxQe4f+ADfPrJhItaVwiB3W6/4DPtdDrx\neErLezRu3JiYiAgKDh5EFmWvkbNrO2HaYLx03jhlZ7GyvoJCZbkUIdYnhRDZV8MYBQWFq09WVhY/\nzpnDD/PnkZeXjxAy3bt0ZfTw4XTq1KmqzasWyLLM1q1bSUpKwmAw0LFjR4KCgi54XFxcHM+Pe5Fm\n+vb4+pwV1jRpvQglnPjUwzx4/0Os+m1lmQ203W43Lz/3Ko10rQg0nY02+fr5Ys224a8Joq6nITuS\nttA7ZgAh7locZBey8FCDMPSaoqwQp3CQ4jlJjjoNr3w1Ho8HtVqNRqshMTcetUNHM3V7VGeiPDpJ\nTz45+IsgJI83kqBEm5/T+SdxmK3ce9+9pWzev38/U2f+wKpff8UjC4wGPff2H8CIYcOoVatstfrz\nefG5Fzm+5STt/LuV2KKLCWhMLXc0syfOITw8rFTrn39ISUlh1o8/8uPChVgLC5EkuK3HLYwaPpxW\nrYq631mtVhYuXMiMyT+QnJyMENCqdUtGPvwQvXr1QqVSIUkSX338CbcPHEhmRjbBzTugObN967IW\nkLtzB6r98bQP702uPRu9r5YmTZpc1DUqKJxPZR2wzUADoOq7WCooKFSa+Ph4ho4aiSMygsB7BhIe\nHIzH5WJv3F5GPf88o+6+m2efeuqGzlNZsmQJn3zwKc4cN0bhjUdyk0c2t97ekzffeQNfX99yj530\n9STC5br4GspWNY/ya8DOlE2sWbOGO+64o9T4H3/8gWyBQHPJrb4agYHk5cTjkXUEqII55ThOUs4p\nVB41LY2dOe48wB7PJvylGqg9auyikFoBdbk9ZCAHCnewceNGunfvTv369cm2ZdJJ2wubsJLiOkWB\nJ4/b5E6Y1X6c8BzCR/jj7fYlVB1MakEyae5TCD8XP8yaXtyy5x8WLlrE6598gqlta+o++ThakxFH\nbh6Ld+xgwaD7mPLFl7Rv377C+33ixAnWrd5AZ79eZT53eo2ehqYWfPP5t9w36L5S1Y5xcXE8+Nij\niPoxBD8wFEOAP267nb/2xLH28cd48dHH6HfHHQwb/AB58VZqGqNpGNgWgSBl/ylefvx1Vvf9lY8n\njEetVlOrVi1+XbqUm7r34NT2vRgDgxBCIOfmE2WsQ9Pw29GotOwt/JvHnhl7RaovFW5MKuuAPQvE\nSpJUAPwG5J4/QQhx6VmaCgoKVw2n08mDjzyM1KEdNVu2KH5drdUS2qY1rkaNmPLDLBrGxNC3b98q\ntLTqmDlzJp++9TmNja3x9z3rbLg8Tnat3M+Qg0OZu2hOmQnjFouFDb//SWdzrwrPESxFMmfm3DId\nsAMHDmB0+JR6XW8wEB4ZTvLpZLSyDh/hR2ZBGjrZi0yRRqE6n661bsHPGAiiSDbin2bEJqcvBw4c\noHv37qSlpRGoDuW44xC5cgZBRFBTikGHHp3HCELgkhycUh9Fo3YRXS+aJ4c+Qr9+/UpttcXFxfH6\nJx8TMWwoxsCAs7b6+RLZ8xZyo6IY8/RTrF22vMK2QMuXLSdQhKJWle/I+BsCOZbnZseOHSUcOovF\nwsjHH8PUqycBDc725dQYDIR1aI+jYQM+nDSR2Bmz8JzU0DKgY/EcCYkIc21C5Uj+XL6ZSTGT6MWu\nxAAAIABJREFUePyJxwGIjIxk7W+rGXz3EORMFeGm2oREhqNRaUgtSCLRdYwed3ZjxINVL+ZZXTl0\n6BDr168nP89CzVqR3H777fj7K+2WzqWyOWBxQDNgOkUSFJYyvhQUFKoh69atI1enJegc5+tctCYj\ngT178PXUKZeUx3O9k56ezsfvfkorn074G0tGerRqHY0DWpJ/3Makid+VeXxOTg46tR6tuuLej946\nH9LSym6VUlHk0c/Pj7rRdTH46rGLQo459rNb3oRsdtAt+jaiAxoSaAwi0BRU7HwVIVCpiv7Up6el\nI+kEVjmfpnQgUorCR/JDjZpaUj2aSR1x4yLUL4znX/0fi5YtYPDgwWXmOX0/YwZeHdqVcL5K2Fu3\nDlLdOixYtKjC+5GclIJBunBhglEykZmZWeK1pcuW4QoNLeF8nYve1xdD+7bs2Luf+n5lJ/KrVWoa\nerdg+uQfcDrP1pVFRUWxYvVyBo+7h2T9cbZa1rIhZyWiXiFvffEa4z/9qPi+KpwlNTWVwfcM4b5+\nQ5jz0U+snrSer1+bTLcO3fnog4/KzL27UalsBGwkRZWOCgoK1xmLVqzA2LTifBX/etEc++VXEhMT\nbzhxyPnzFxAgB2PSlp9UHeXTkHmz5/HU0+NK9ZHz9vbG6XYgC7lYfft8Cl0F7M+Mw+q28MSzz3JT\nhw7069evuNqwRYsWzNDOKvf8RqORyJqRJPoc5O03XuXjNz+lk//N5TpuQggs2pxiXS29QU+WLYN2\n+puR3Co8sgdJgEDgwYNOo6exujW7LZsxGM5XGTqLy+Vi9e+/U+/pJ8qdA+DfsgULVyzn0YcfLn9O\ngD9O2VHu+D84cZTSJlu4YgXmFhVrhmkiInDKMi7ZeZ5jehYfvRlNvo5t27bRtWvX4teDg4P533P/\n5elnniI/Px+NRlMt5DKqK9nZ2Qy+ewjadG+6nLel7HDbWThlKfn5+bz3wXtVaGX1oVLuuxBihhDi\nh4q+rpahCgoKl0d2bi56n9LbW+ciqVTofHzKVEP/t7N5w2YCtSEVzvHW+SC51Jw4caLUWEBAAC1a\nNyPZklhqTAjB7swdLE9dRUoDLwy9evC3Ts378+fRqWdPfv31VwA6d+6MKchAWkFKuTYk5icQ1bAu\nw4YNo0792pzOL23LP6RZkzGHeNOxY9HWmyRJ+OCHTmVAp9dhMOjR6nRIkgqDQY9Op8Ok8kYvjGi1\n5UfybDYbkkaDpgInDUBn9iE3N6/COXf07UO2Oq3CqKvVacGldZTKJ8vJzUV3gWdaBtR6Q3Gj7/LQ\noiv3uddoNAQEBCjO1wWYOmUqnhQ1MX6NS30o0GsMtPLryIqFP3PgwIEqsrB6ocRPFRRuEEKDamDP\nyalwjpBlnLl5pZKtbwRkWUa6iD+JKklVrszBw088TKLnKHa3rcTr+7J2c8yYTdCwofh160SdDu0J\nadmC2vfeRY1Bd/P0G6+zefNmVCoVH38+nmPyXpItp0o4JUIITubFk6KN5/2P30OSJD789ANOa4+T\nmJdQam6yJZF4sZ/xn53dKnPYHQToA7F7ilJ1JUlCrVYhSWe3P22eQoK8grFYys8oMZlMqIXAZbWW\nO8dus5F4+DCnTp/m9oEDeef994mPjy81r0mTJtRvVo9juWW/KXtkD4cK4hg+6oFSUceQi3imVULg\ncdjKjX79gwPbDfncXymcTidzZ80nyqfs7WAAjUpLkAgndmbsNbSs+lJpB0ySpEGSJK2RJClRkqT0\n87+uhpEKCgqXz30DBmKL21fhnKwDB2lcr165vff+zbRs25JsV8V/wuxuG3Zho2bNmmWOd+/enbHP\njGaH5U8Sco/ilt3Y3Tb2Ww/he/uteIxQu05tVOdUznmHheHfuxdvfzweIQTt27dnyuzJFIZlsTr5\nJ36JX8wv8YtZnfwT6mgnsxfMolGjRkCRbtXs+TNR13OyOXcN+3J2sD9nJ1vzfscRmcfU2Cm0a9eu\n+Fxe3l6YA3xQG1QUuq245bO9I92yC6u7AL2XDnOguVg9vyw0Gg139ulD+s5dpQeFIDk5meMnT5K+\nOw6/tq1I9DIycdlSOvbsyVPPPlsiD0iSJL6e9BVEOtmT/Re59uwzywhSLKfZnvsnbW5tweNPlG7d\nM3jAQAp2x5VrJ4DrZCJ6lbpYcqMscu3ZaHxUtG17wf7JCuWQmpqKcBb1H62IGoYQ9uys+Hd2o1Ap\nB0ySpKHAD8AxiloRLQNWnFknH/j6ShuooKBwZejatSuRJhPJf24qc9yem0vOug08VUG+zr+ZwUMG\nkUkKTk/5+UgJeUfof9d/KhTffOzxx/hu9kQiu9bgz9xfWJ20GCkmEr/IIOrFRGMsQwk/oH4Mp7Ky\nirdm0tLSyMrKxlcTQIgmghB1BH66ANLT0kslojdp0oQlKxfz49JZPPbuaB55ZyTT5n/Pqt9W0qZN\nmxJzu3XrRp42izpRdQgKr4Fb7cTizsMjPHi0bkIjQoioHUGelEWXLl0qvF+jRozAsWM3lqSkEq+n\npaeTY7XiysrBEZ9A6p44MrOykBo3QNOlI9NWrqBZ+/YcPHiw+Jjg4GAWLVvIiOeHcsJwkPXZK1iX\ntRw5ysobn73CV99+iUZTOmW5T58++BQUkL5zd5k2WtPScWzfQY+uXTiQu6vMbU6nx8Ghwj08Mu7h\naikpIcsy69ev5767BlGvdj2ia0Uz8M67WLNmTbVKaJckqVzx2nMRQpT4AHIjU9kk/OeAd4APgbHA\nt0KInZIk+VAkS6FIUCgoVFNUKhXTJ33HsFGjOJGcjG+b1niHh+G228neuw/brjheGTeObt26VbWp\nVUKdOnUYOnIIC6cupoW5AwbN2QiQEIITeUdxBFp4fFyRVEFaWhoLFi5kx969qFQqOrZuzd133UVA\nQAAdO3akY8eOOJ1OXn3zTX63FRAWHlbuuSWVCn1oKCdPnuTEiRO88vRrNDW2wzekZNl+VmE6T4we\nx6QZ3xa3F4KiN78mTZpcUBS0fv36NG3dhIRdR4gJbExgYCCyLGM0GoipH4MQgoO5u7nl9h4XbDsU\nExPD1x9+yJMvvkhuowYEtGyB2mQi+dAhHImnKdx/ALXZTMj9g9Cck6fl064NeTt2MXjUSBbPjiUq\nqqiBitlsZuzDYxk9ZjRWqxWNRlNhFA6KihJmTv6eYWNGc/LESfxat8QUHITLWkj2njic+w7wyetv\n0L1bN8Y8NJbtu/4kTF2bIFMIHuEhpeAUadIpBo26jwceeKDCc1UFbrebMSPHsGrJL7jtHvxURXIe\nf/6yic3rttC9dzdm/zirTFHfa014eDhGs4E8e065OngA6Y5kbuva/RpaVn2p7BZkDLBJCOEBPIAZ\nQAhhAT4CKi6JUVBQqFJCQ0NZtmABr9//AL6795I8eRp58xbRNyySJTNnMmzo0Ko2sUp54cXnGf7k\n/Wy3/cGe3G0cztrPgczdbMlbi6GBxNxFcwgJCeHbSZO4+T/9mPrXZg4HB3Iw0I9v1q6ha+/bmDN3\nbvF6Op0OH29vZKfrgueWXS4kSeKtV9+hibFtmW9igaZg6qmb8cbLb12yVMiELz/FFVzAvqydWJ0F\nZ/LDJCyOPPZkb8MrSsc77719UWvdfPPN/LJoEcOat8S+fBWHJ3xB3uo1BNcIRKXTEfrAkBLOFxTp\nzhnr18PdpBHjP/+s1JoqlQofH58LOl//EBUVxS+Ll/Bc/wHoNm8l6bupFCxeyj0xDVg5bx5977gD\nb29vZv74A+9+8yZezVTscm1kP3/TsE9dps2bwosvvVAtxYdfeekVlsxbRpijLu21PWikaUUjTSva\naXsQ4Yrmt+VreHrcM1VtJgBqtZrhI4cRbz1c7rNpd9vIklIZcn/ZHQ1uNCobAcsH/vlfkQQ0Ataf\n+VkClAxGBYVqjslk4p577uGee+6palOqHSqViqeeHsdDIx/kl19+ISH+BF5eJrrf3J2mTZsiSRLT\nZszgq3lzqT12FLpztyKbNMaencPb33yNyWSi/513AtC9a1fmv/sO3FT+lp6r0IbzdBJWqxVVoQY/\nc9naWgAhXmGcTDrMzp07S20xXgyhoaH8tHwR33/3PXNnz0flUNNMrsNh1S7uHzeUUaNHVaq/YURE\nBP995hn++8wzTPj8c2YeOoDsdmNq0hj1Oc28z0VSazA3acz62Hmkp6dfdpNvs9nMsPvvZ9j995c7\nR6vV0rt3b3r37n1Z57pWWCwWpk6aRl0aEa4tKQmjltSEa2qjdquZM2sub7/7VoVit9eKEQ+O4Nef\nf2P/gZ3U921aovAhz57DgcKdPPLsWOrUqVN1RlYjKuuA/Q20AH6mKP/rdUmS3IATeB3YemXNU1BQ\nULj2mM1m7rvvvlKvFxYW8tmkSdQcfn9J5+sMhgB/Qgf8h/cnfEp4WBi/r19PTn4+ttNJpGz7m7D2\n7UodA5D650b69OxJamoqBkfFzo8kSXgLX44ePXpJDhgUSWa88NILPP3s0yQlJXHs2DE2/b2xQumJ\ni8Hs7Y2w2bBkZqGPrlPuPCHLaA0GjGEhJCQkXLYD9m8kNjYW4ZAI05Zd8AEQrI4gwXWYadOm8fzz\nz19D68rGZDIxa85M3nrjbX5ZvhpfAlALNXaVDclL5vl3/svgIeU3dL/RqKwD9gFQ58z3rwO1gYkU\nbWX+DdyY2bsKCgpXDKfTidVqZdWqVfj5+dG2bdtqkeMCsGbNGlThoRgCys9x0RgMHIpPYPATj2Nu\n3RKN0Yi+eVMOzJ1P0ta/aDF6JFqTCVthIdacHLK2biPMUsCrEz5nzpw5FHXCrhghiSuiwq7X64mK\niiIxMfGynS8o2pL8dOoUCAxAeMpJyJYFwunA29ubfI+sqMmXw+7du4uao5cj6gtFzniAHExcXPWp\nKvT29ubjT8fz0isvsnnzZgoLCwkNDaVz585lFlLcyFTqbgghtnImyiWEyAX6S5KkB/RCiBtPuVFB\nQeGKIcsyU76fwpSJUxk5ZiSxX87HiR1hdDP60VGMHjO6yt+sTyQmIgUFlTvuyM9n5/dTMXXpRGjX\nziV0pcJuuZl9s2LZ9MrraIOC8bjceDKy8dN4keFjYsLHE+h5W08smhkIIcrNSZKFTC5ZtGzZ8kpf\n3mVTr149WjdqzObEk9iPx+PdpFGpOU5LPr4+ZmS7HVd6Bg0aNKgCS6sHHo+HrKwsJEkiMDCwxPOt\n1+srdL7+QSWpSumjVQcCAgLo169fVZtRramsDMVISZJKSAELIRyK86WgoHA5CCF47ZXXmDx+GvXl\nVphU3jQzt6WNuSv15VZMHj+N1155rcp7VBp0OoSzfEX1xD82oq0XjXezJqjPcxZNZjP17rsHWaun\nbqYPPWnD4FpD+E/Ne+jg3YP18zbx+SdfYA7xIaXgdPnnyD9Oo2YNqF+/fMHLquTzjz4iUlJh3bcf\ne2pa8euyy4UzJxedLAgPCyN142YG3NHnhlSXl2WZr7/+hs7tunJr197c0rkXPbrcwvTp07Hb7UCR\nxEYeWRU+80II8qSs6yavTaEklf04ORFIlyRpmSRJQyVJKjvDUkFBQaESbNy4kZ8X/Eprv86Y9b4l\nxsx6X1r7dWbVgtVs3LixiiwsokuXLriOHUeUoYQvu92k7NiJT+uWyA5HcX/Hf/C43aSmZRDQtiMu\nDYR4h6NVF22tGjRGmvq3Jf1gDu06tuGk6hAn8+JL6Cp5ZA/xuYfJMCbx/sfVt5deUFAQyxcsYEjf\nvqTPmEX+rt3Y09KRc/MIMpupHR5O8roN+KWm89+nnq5qc685WVlZHD92nDkTFhLjbk5X39u4ya83\nYZZovntnGg8MGU5hYSG33XYbXkEGMlyp5a6V7cpA7QsDBgy4hlegcKWorAMWAjwG6IAZFDljCyVJ\nuluSpIqbgikoKCiUw4wpPxAm1UajKjsPSaPSEibVZsaUqm0327hxY2LCw0nbsbPUmCMvH0mvA7UG\nb5MJ7Xl5azk5OaiFBq/wSHI8uaWOlySJaK+GrF+zgWmxUzE1ltiSu4Z9+dvZm7+dzXm/EdTGh3mL\n5xAdHX3VrvFK4Ofnx5TvJrNk2nRqJ5xC9/sGvA4dxf7HRk5MnExnH18WxcYSEFB+tee/lWfH/Rfh\nlGgR2B6z3q/49QBjDVoFdCIlLpO33ngblUrF15O/IlF/iExXGi7PWSkTl8dFliudBN0BPv36E3Q6\nHR6Phw0bNvD6q2/wv2eeY+K3E0lNLd95U6h6KpsDlgtMA6ZJkhQI3APcB8wDCiVJWiaEGHblzVRQ\nUPg3s3XLX3T2ubXCORE+tdi8Zc01sqhsJEniy/Efc+/wBzhlKSC0Ywe0piJlHretEFe+BcluJ+KM\nuOi5WCwFaCQtbo8HVTmffX30vsj5Ai8vLxYsmc+RI0c4dOgQKpWKpk2bXnfl+7feeis9e/Zk9+7d\nxYn+bdu2vWGrHo8fP86uv3bTs2vZz7okSTT0bc6qpT/zwkvP07dvX76bPZH/PvkcaVmJGB0+SEjY\ndBakGh4+G/8pgwYN4sCBAzw25nEKM+z4eoLQqrT8LXbzzYSJDHrgPl5+9aVqqfJ/o3PJJQlCiCzg\nO+A7SZL6ApOBIYDigCkoKFQKj9tdYa8+AJWkRq4GrVdq167NkjlzmfDVV6yc+B36oCAQAmdmFoE6\nPaF6A5oyKgqFEEhIFB4/ToS2/ER+tUqN213Uo7F+/frVNtfrYpEkiVatWtGqVauqNqXKWbduHX6e\nIIpkM8tGp9bjSwAbN27kzjvvpH///vTq1Yuff/6Zv7dux+12U7deHXr37k1UVBQJCQkMHzSCCGc0\njX1L6oW5PE6W/bAKp8PBO++/c5WvTqGyXLIDJklSM2AQRRGwaOA48P4VsktBQeEGol5MDJmJ6YR4\nl9+uJ7MwjXox9a6hVeUTHh7OJx98wKsvvEB8fDySJFGvXj0WLVrEJz8txLdWTaTzkvCNRiM5GWkU\n7t1PTFDZSdMOtx2bbCMyMvJaXIbCNcaSb0HDheU+1LKGwsKznf1MJhM33XQThw4eZuGchbBSYvLn\nU/Cr4YvepMfXGkxEYO1S62jVOlr6dWTpguU8NPqh4rZPCtWDylZBNpIk6Q1Jkg4AuymKdi0B2gkh\n6gshXrsaRiooKPy7eWjsCE674sut+BJCcNqVwINjRlxjyyrGz8+P1q1b06pVK3x8fBg6dCjNA2pw\n8qelOPLPFocLIdBaraQtWUgTQww++rIr/xLyj3LHnbffkJWBNwJh4WE41fYLznOobSW2aRMTExnY\n7y5+nbaeFtpOdPK9lc6+vQjOqcO+Pw5zOuckHtld5lpatZYaIpw5sXOu2HUoXBkqGwHbD6QAC4BR\nQogtV94kBQWFG41+/foxe0YsBw/upqFfixJjspA5lLuH8EbB1V5XSKfTMW3SJD757DPmTfsBTUgw\nktGIKyMTP7WaPu07krAjEafHUaJNixCCU/kJFPhk8cRTN15LXYvFwoqVK9m6YwcCQdtmzenfvz++\nvr4XPvg64rbbbuP91z9AUI5ILWBx5OMxOOnatStQ9Gw8OuYxzDlB1A08ux0tSRLeGjMN1M1JsiUQ\nl7qDVuEdylzTTxvIwX2HruzFKFw2la2C7AFECiGeVpwvBQWFK4Ver2fG7OnU7RzJ5rw12D2FxOcc\n4WDWHjbnrSGqS01mzJ5+WYKTLpeLP/74g/nz57NixQpycnKu4BWcxWAw8OpLL7FqwULu7dCJ3nWj\nGTd4CGuWr2DOnFgGPNiXvyy/sy97O/E5RzictZ9t+RtwRuTz48LYG277ccnSpXS6tScfLVrAVpXg\nLxVMWLWCzr1uZfaPP1a1eVeUgIAAhgwfjM1TiLuMiJXT42C/dQePjnukuPvDjh07SIlPo45vTKn5\nEhJIErXV9UnIPlqiUvJcZOFBq1VU6Ksbla2C3HC1DFFQULix8fX1ZfrMaRw5coTdu3bT9t4mBAYF\n0rdf38tKRBdCEDtnDp9PnIjLxxtVYADY7Djeeos7b7+d1196CZPJdMWuw2q18tb777Pi11/R16kN\nBj3ynt18N3Mmzzz2GC+/+jJjHh7DsqXLOBF/Ei9vEz169qB9+/ZXVOnf5XKxbt065vy0iLSMTPx8\nfbm7b1/69OlzRa/3fJKTk5k7fz5//LUVl9tN84aNeGDIEBo3blxq7s+//MKLH31I5LChmILOaSbd\nqiX27BzemzQRvU7HvZfQOF4IQUpKCoWFhQQFBVWbaNpzLz7H3Lnz2Ja3nmARQbBXGLKQSbclky4l\n88DYoTw08qHi+b+t/o0AT3CZnRH0Bj2oBFp0mISZjMIUwn1qlZqX6UllwK3Dr+p1KVSeSrvEkiR1\nAkYB9YFS2l9CiPZXwC4FBYV/Aenp6fz888+kpqfj5+tLr1tvvWAicP369UlOTubdD969IjZ88fXX\nTF78E2H3DMQr5GxejavQxs9r1nJ01Chip0/HYLh8KUObzcawkSNJ0Kio/ejYYokKAGtaOu9N/o7M\nrCyeeuIJRo8ZfdnnK4/k5GSGjxlDupAxtWiGsV4UeRYLb8+eyfgvv2T6xIllOkSXyw+zZvHhV19h\naNwQc/OmSGo1v51MZOmYMfTr3p333367uB+gx+Ph7fHjCRvYv6TzdQZDgD/hdw/k/c8+o/+dd150\nP1AhBMuWLWPi9OmcTE1BazLhzLdwc5fOjHv4katy3ZVBo9EQGRnBjIVTmTl9FnG74pAkFR27tGPY\n8E9p2LBhifn5+Ra0qrIjv5IkERAYQE56Lhq0uMqIquU7crFochg4cOBVuR6FS6dSDpgkSb2AVcBa\noCvwM2AEugCnASVCpqCggMPh4I133mHp6tXo69dD8vNFLrDy+bSpdGrZkgkffoSfn9+FF7pMjh8/\nznexs6k9eiQ675LK9FqTkVr/6cuR+YuYHRvL6FGjLvt8s2NjOeZ0UGfA3aUiFl4hwdS6fwiTpkzj\nP3fccdUq0goLC7l/1EgKYqKp07lTibHARg3JPHCQYWPHsmrhQkJDQ6/YeZevWMGHk7+j1sgR6P3O\nRpvMtWri6dCOVQsW4T3+I15/+RUAtmzZQoFWQ1DN8rdcvUKCyQj05/fff+f222+/oA1CCF5/+20W\n/bmBwJu7US/qLiSVCrfDwY5du7l35Egmjh9Pt27dLv+CL5OWLVvS8osL9/OsVbsmm8X2cseDgoKw\n5FvItWah5qyUixCC1IIkjrv388EX71WbCKDCWSob734b+ALoe+bn14QQt1AUDXMB66+caQoKCtcj\nsizzxLPPsPLgfuo+8Qi1/tOXmjd1pXaf3kQ/8Si7nA7uH/lQiTL7q8XsuXMxNm9Wyvn6B0mSqNG1\nM9Pn/IhcRnuhyiDLMlN/jCWoW5dyG2nrvL0wNmtK7Ny5l3Wuili5ciXZRgNh5zlf/1CjcSNETDSz\nYmMv+RzHjx/nw/HjGf344zz13HOsXLmSDz77jJD/9C3hfP2DWqej1t0DmbN4Menp6QCcOHECdWjI\nBc8lhQQTn5BwUXatXLmSRX9soM4D9+Nfr16xFIhGryesYweC7xnIEy88T3Z2diWutmq5s/+dZEmp\nuOWy87tUKhW+Yd6Yw704oTrEbssW4izb2Jq/FncdC9/O+Jq+ffuWeaxC1VJZB6wxRVEvGRCAF4AQ\n4iTwJvDKlTROQUHh+mPjxo1sPnSI2ncNQHNe0rxKoyGyV08SgQULFlx1WzZt24Zvg9LJy+fiExFO\nTmFhsWNwqaSmppJvd2AKDiYvN5fsrCzy8vJKicf6NqjPpr//vqxzVcTM+fMxt65Y9DSoXVtiFy6s\ntNPpcDh4+rnn6DfsfuYfPcSBAF+2CA/PfjaBuAMHEKL89TQGA/r6MaxYsQIArVYL7rKlE0rgdqO/\niO1HIQQTZ0wnoHvXUs/dP/hERqCqU5vFS5Zc+LzVhIiICP5zdz/icv/GI5cWIi50WTni3Mvn30xg\n8/aNfDj5Xd78+hXmLItl2c9Li6spFaoflc0BswNqIYSQJCmFIgHWP8+M5QM3VvmOgoJCKabHxuLd\npjWqclqfSJJEYKf2TImNZfjw4eVGi64EsiyXEkQt0yaV6rIjYE6nk5zcXA4dPFy0FSQkkARJeAgI\n9CckNBRJkpBUqnL1zs6nsLCQU6dOIUkStWvXvqgq0NPJyYT07ln8syM3D2dBARqjAUNAAJIkYQjw\np9Bux2azlWoaXh5CCP774gtsOHmS6McfQaU5+/ZhrBeFNboucTNjaT12FF4hZUe2NDVqcDIpCYB2\n7dph/2wCsttdYq0S55RlXMfiaffM/y5oX0ZGBscTE4m5q3+F88xNm7Ds19WMGjnygmtWF956502s\nBf/jj9XrCCGCAGMwsuwh3ZFCliqVZ197uliipTpsrypcHJV1wPYAjYBfKcoDe0mSpCTASdH25N4r\na56CgsL1xt6DBwm8f1CFc3wiIzmcmYHNZruqFXktmzZlffwJvMPKV9gvzMxEj0RQUPntgS6ELMt8\n8N6HFKRl4WtxY/A7K6QqC5nczDycThe1atUk73g8t1wgETwjI4NvvvuORSuWI3l7gxBIhTaG3n03\nj44dW6FQq8loxF1YSEFyCifWb8CSmobG7IPHasXgY6b2TV0IbNwIIXsqJetx4MABfv/7b6IeGVPK\nYVKpVBhrRkK7NpxYu54mQ8v+/XvsdrzP/L6joqJo1bARR//6m/AuZW+Xpu/aTVRwCM2aNbugfXa7\nHa3ReEGHW2MyUlhou+B61QmdTscXX3/Brl27iJ35Iwf2HkSjVdOnxy0MGTqEmjVrVrWJCpdAZR2w\nz4G6Z75/GVgOrD7z82lAKbNQULjBUalUCM8FoklCIHvkqxr9Ahg+ZAg/P/4YnnZtUJezjZWx+S8e\nvPfeoi2xS2Tt2rVsX7eLpt5NSNyzB0P3HsVjKkmFUe2FNb+A3KwsbHviGD5xUrlrJScnc+8DD2Ct\nFUH4yBHozzhb9uwcYjduYs3Q9cyfNQt/f/8yj7/j1luZsmwFOWnpmG++ifCBdyKp1QhK3pchAAAg\nAElEQVRZxnbiJEfW/o7P9h306tyluCLxYoidNw9ji2ZlRqu8vLyQXS5MTRuTNmUGLqsVrZcXLqcT\nu71I+d1gMOA8dJieDz9afNzH777L3cOGcdrpIrRTezRnKlHdDgdp23fArji+nDnzop6TwMBA3NZC\nXIW2EtWn52NNTaPZdeiwSJJE69atad26dVWbonCFqFQOmBBilRDimzPfJwFtgAZAS6CeEGLHlTdR\nQUHheqJjmzbkHDlS4Zzc+HhioqMwGst/o7wS/J+9u46Puv4DOP663u5267GEFaNbUkJCumN0CEiK\ngAmIrT8DRQmVztGNSEuHSHfHeqz7tsvv7w8UmWtWIN/n4+Ef3vd7n8/nju3uvU+83zVr1qRTs+aE\nbNiM8V+zHoLFQuSRYzgkJDJ8WNFKHC1duAxPmS/VHGsiufGAxPPnEJ5Y0pRIJEgNFm6uWEXXV16h\nRo0aubY16f33MVSrQoX27R4HX/AoLYNPty7Euzoz/bPPcn1+i6ZNibl+E6fAXthUrYLkr6VgiVSK\n2s8Xl36BJASH0LBO/ifwnnTr/j00uSSJlcpkONjZYTEYkdpouLt7Hyd+nsfJX+Zz9dcdBN+7y4Ud\nO0mPiclSYsfLy4uta9bQzEbLg5/nE7Z2A2HrNnL/p/k0kMjYsnp1gU+LajQaOrZpTcz587neIwgC\nuouXGRwYWKjXLhKVhCKlxhUebWS4U0xjEYlE/wGvDRrE75MmYqpbJ8fN0ILFQuLJP5k8suTyYP1N\nIpHw9RdfYPf996yZtxCFvx9SJwcEXQb6W7epHVCJOStXFiklhiAIXLpwiWZ2HZBL5bzq3o4T544T\ncekSVtWqILW2whybQOadu8gx8tXnX+Q6o3Pz5k2uPbiPf6exufbn/koLDs6dx8OHD3NMI3H42DG8\nWr2CyWzGpNMht7aGv/ozZWRiTk/H89XW/HHuHGMK8TqVSiUWgyHX625ubkTv2UtacAgWGxvUtWqg\nksvRh4YRtXYjUrMF51av0HvwIDYFrXq8bObh4cGcmTOJj4/nxo0bCIJA5cqVswRqBTXu9VHsGzKE\nJE9P7H19slwTBIHw3w/gb+9A8+bNc21DEASuX7/O+fPnsVgsBAQE0Lhx42JNkisSQQECMIlEMr4Q\n7QmCIMwrwnhEItFzrm7dugS2a8+m1evw6N4VayfHx9cMaWlE7tlHfU8vunfPe7N0cZHL5Xw4dSrj\nR49mz549hEdGYqvV0nra9CJl2H+SRRAelYUB1AoNbT3bk5gZT+TNMAxCGhqZBg+3TpzTHUWWy+EE\ngGPHjqGsVDHPfUwypRIrf19OnjxJr169sl3fdeAA5Xt0BbU1MXFxJN++i0WvR6JUYOPqiqeHB5qK\nFTnx3Q8YjcYCL722b/EKs/bswrFyzu9Z/PUbJJ85h3NgL+SOjkhkUkCCvLoW25o1SN5/ABQKLLVq\nMPWTj1m9dFmW5zs5ORX5xF5AQABL58xhzFuTSfZwR1ujOgq1mvToGDIuXcbf0Yml8+bl+m9w+/Zt\n3vvwQ+5ERqD09wWpDPPqVdhaLHw5/UNatWqV4/NEoqdRkBmwnwrRngCIAZhI9AKTSCR8Mn06Hkvc\nmLdsGYKTA1I7OwSdDmN4JP16dGfqu+8Vav9RcXB0dGTgwIHF3q5EIqFa9WpE347EQ/vP3iIHKycc\nrJwe/39kaijVque9+V6XkQHK/DfGS5Sqx3ur/i0zMxM7aytSQ8OIO3SE9IR45La2mNPT0aus0DRv\nik39l5BIZRgMhgIHYD169GDm/HmkRUVlO9QgCAL39u5D26IpCicn1O5uj9JvCCCVy0AiQdmrO2FL\nV9B48kTOLV3BgwcP8PX1zaW3p9ewYUOO7tnLrzt2sH3PHtJ1Oip7eDDo409o2rRprjNZd+7cod/w\n11A1fRn/Hl2yBMHJD4IZ/8E05nz+BW3bti32MYteTPl+AgqCIM67ikSiQpFKpYwZNYrXhg7lxIkT\nxMfHo9Vqadq0KVqttqyHV+xGjH6Nzyb/D3fBK8flRUEQiDAF89noj/Jsp7yXF8LRw/n2Z4mLw9PT\nM+c2PD25te93om/dwq51Szz8/R6nvsgMC+fewcMk3X+AxtqqUHvw7O3tmfn5F0z6+GPs27TEqVrV\nx6lGYi5dJiMlFTs3NwQrK5BIsm3Wl2k0WPn7E3P5KtYV/Tl79myJBGAAWq2WQQMHMqgQAfcnX32F\nvFEDytXLvjfOztcHaZ+eTPnsU1555ZUCl0USifKSb3AlkUj2SSSSyv96rLVEIilY8hiRSPTCUqlU\ntG7dmsDAQDp06PCfDL4A2rdvT5UGAVxOPIPRnDVjudFs5FLiaao1qkS7du3ybKddu3aYQ8PRJyfn\nek96dDTKtHSaNm2acxstWhB+6k9c+geiCfhnOVMikWBdoTzl+vfl4c1bvFzvpWyzQRkZGURGRpKc\nS//t2rVjxZw5eIVGcP+n+YStWU/IspXE/boTZ18fHB0dQZr7iUWFazky4uNBJsVszp5UtKw8ePCA\nCzeu45pHAlutpycmRwd+//33UhyZ6L+sIGsArwKPa0tIJBIZsB9oAOR+3EQkEonyYLFYOHnyJDdu\n3EAqleLv709CQgKxsbG4uLgQGhpKhQoVynqYBaJQKFiwZD6ffPgpu3fswcHigtyixCQ1kCSNo0OP\n9nz+5Wf5Lrva2Ngwdvhwftm0Ge8B/bKlU9CnpBC5ZTufvvlmrm1FxcZgW6c25LLPySJY0NarQ0xi\n4j/t6vW8O20aO/fvQ6pSYcrMpHa16owdPpzWrVtneX7Dhg3ZGBRESEgIERERWFlZERUVxYdLlzwq\naJ6amuvrEwwGJHI5xogo1Go1QUFB6HQ63NzcaNOmDTY2Nnm+PyXl+vXrWHtXyDUh7N/k3hU4f+kS\nnTp1KqWRif7LnnYTRskm7xGJRKVCEAQePHhAXFwcWq2WypUrl8ppr+PHjzPl009JkUqQeHkQf/M2\niQ8eoPbxxiUggDdbtaFdYB+avVSfGV9++Whm5RmnVqv57ocZvDvlHfbv309CfAJOzk60bdu2UCf6\nxo8ZQ3paGssXLsaqejW0fr4IgkDa3XtkXrvBW2PG0C+PNAoHjh2nStdOPExPwxAXj9TaGolcjmAx\nY8nIRGo2U71VSy7O+QWj0ciZM2e49+ABh1KS8Bk/FoXaGovZTNiNm0z47FOGX7zIe2+/na0fb29v\nvL29AUhISCDzk09wlcnBZMoxu70gCGTcvoNDtWokBIcw5X9foqoUgKBSIUlMZPpX/2P00GFMGDeu\njE4cil9rotJVurtgRSLRM+PgwYP8MO8X7kdGoXKwx5iWhqPKivEjRtCvb98SS5J67NgxRr/3Li7d\nu+Lr68OtrdvJlErwmvwmEoUcY3IKClstFd8cz/kjR+n/2jA2rVqdZ/b3Z4mrqyuDBw9+6udLpVKm\nvPce/QIDWbN+PeevXkUikfDySy/R76tv8PDwyPP5er0ee60NAW6upKWlkZCUiDEjA5lMhoOLC7a2\nto/ykslkREdHM+6dt3lj0mQ8m/+zpCmVyXCpUR17Pz+WrgjipTp1ss2EPcnR0ZFOr7bhwLHjeDRu\nSER0NEpHRyTyf2bhdDdvQbqO4N17KP9qa/w7tM8SpOmTk1mwdTtJSUl8PL10ywpXrVqVjJBQLGZz\nriW0AMyhYdRpX/DZr9u3b7N9xw4iY6JxtLOna6dO1K5duziGLPoPKGgAllPhsoIVMxOJRM+clatW\n8dW8eTi3b4N/z26PN2mnhoXz+eJFXL91i88++qjYgzCz2cz7n3xCue5dsfP1ITU8gugbN3EbMRTp\nXxubBQEMBuOjwt1tWvNg63ZWrFzJmxMmFOtYnnU+Pj58MGVKoZ/nXaE8cZGROFaqhI1Wi00O++50\ncXFoNWr27N2LxMcbqUoJ+uyFsRVqaxyaN2XesmV5BmAAH0/7gKtDh/DwxB841axOQnw8KJWPZu+u\nXiP9+Ek0EimOjRoS0KVztuer7Ozw7t+XtQuX0Ld3b6pUqVLo1/60/Pz8qFWpEsEXLuFaP+dM82lR\nUUjj4gt0CjI1NZVJ773HH5cvYVW9GkoHB4zhIaybNJFK7u688fqo4n4JoudQQed590okkhiJRBID\nRP312IG/H3vyvxIap0gkKiZ3797l65/m4j1kII6VKmXZpG1boTw+gwew6dBBDh48WOx9nzhxgnSl\nAjtfHwDCT/2Jpk7tx8EXgNzaCgGBDJ0OgHIvN2HFhvWYTNkDBFF2w/sPIOXs+TwLfsedPsvQvv3Y\nvncPtjVzz8oP4Fi1CpevXyMpKSnP++zs7NgYtIrA6jXJ2LoD65N/Ytmzj5SlK6gQHsWMD6bjUaE8\nPq+2ybUNuZUV6to1WbVubd4vsgR88eGH6E+eIubylSxVDABSwsKI2riFrz78KN/6mUajkRFjx3I+\nPZWKE8ZRvk0rXOvVwatFc/zGjiLcyYH7wcGkpKSU5MsRPQcKMgOWe82LQpJIJOWBlYArj2bQFgqC\nMLu42heJRPlbuWYN6to1Udnb5XhdrlJh16QRC1esoE2b3L8sn8aVq1eRlP8nfUJKeAQ27XPoQyIh\nMzMTa7UajWs5HprNxMbG4p5HUW3RI+3bt+eXpUuIPHwUj5Ytss1ixl68hCo0jEE/zGLrnj0oNHkf\naJfKZMitrdHpdPlWDLC1teXDadN4e9Ik7ty5g9lsxsfn0enIiIgIfl6zGrWLc95tVPTn7PFTBXux\nxahSpUqsXbKEtz/4gPvH/0Dh74MglSJERqHO1DPns88LNPt14MABbiTE4TtkULaEuhKJBPfmzTDp\nDKzfsIFRr5d8NQjRs6sgecCKLQADTMA7giCcl0gkWuCcRCLZLwjC9WLsQyQS5eH3o0dx6N4lz3uc\nqlXl3M7dGAyGks95VIDNDHlM5oj+xcrKilWLlzBy/HjuL1mOVc0aWDs5YkhJJePadeyNRpYtWYqz\nszOebm7cj42FCj65tmfUZWDJyCxUuSa1Wp3jXiez2UxcbCwJyUmYTWZkcjmO9vY42Nsj+3s/WBn+\nW1etWpVdW7Zw+fJlzp8/j9lsJiAggGbNmuVZweBJS9eswfalenlWM5BrNCxbuJDXR44s8YL0omdX\nqW7CFwQhir+WMAVBSJVIJDcAT0AMwESiUqLX69Gq8g6qpHI5Upm82AOwWjVrYtm29fH/25X3Iu1+\nMCo316w3CgJWfyUJTYt6iI1S8VS1AV9ULi4ubFu/nlOnTrFh61Ye3n2Ag50dPSdNplWrVo+z3w8O\nDGTKzz/BSw1ybSvmwgU6tmmDWq0u0pgiIiKIePCAzJAQrLw8kcvkCGYTMSkpxMbF4VOhAtZqNSl3\n7tC5bu75uEqaRCKhdu3aT71Z/s69e7g2b5LnPVKlgpi4OPR6/aPUHbnQ6/Xs37+fg8ePYzAYqBoQ\nQO+ePXOsASp6/kjy2idQoh1LJD7AUaCGIAgp/7o2GhgN4Orq+tK6detKfXzPsrS0tDLLl/Mi+q+9\n3/cfPMCgUiG3zv2D32I0YU5MpGrlyrne87Ru3b4NtlpkKhUWgxFdfDwKJ0f4a8ZAsFhwVSpJBhDA\nkJSIi9YWFxeXYh/Li04QBO7eu4e9gwPJOSRQtRgMmBKT8Pf1zXfvU16MRiN37t/DIpNjRkBu96/l\nb4sFwWJBpVBgiIunYhH7K0s3bt1C7uiAJI+cYvYSKQ8jI6letWquM2Dp6emEhocjyGRI/6ouIBgN\nWDIycXJ0xM3VNcfniXJWmp/jrVq1OicIQv387iuTNBQSicQG2AxM/nfwBSAIwkJgIUD9+vWFli1b\nlu4An3GHDx9GfE9Kz3/t/U5PT2favJ/xHjQg1w//0J27Gd6gUYm8bisrK0ZOnoxDp3Y4BARw98Qx\nou8/wKlbJyRKJZaUVKbUqsu29BQiDxzGIzWVDUGr0OSzV0n0dKpWrcqO335j7rat2NSphbqcC8Z0\nHSlXr2G+/4B538/MNet+Qc388UdWXbqAe8sWnJ+/GEl5T+yaNsly+CIjLBzDgcO82SeQ9u3bF/Vl\nlZkde/Zw+OolPJu+nOs9nSwSDp04wYTx43O8funSJSZMnYpTj67Y+Xj/9agAMgUmwUTIsqUMbt2G\nae+/XwKv4L/pWfwcL/VsdxKJRMGj4Gu1IAhbSrt/kehF17ZtW7ytrIn4/WCOJ+Wiz53HKjyyUHX0\nCqNx48YsmzMHxR9neLBoKUq5HI1USsTsn0lcvwnF3fsYU1K4N3ceLzs4snb5CjH4KkFubm5U9Pfn\n2zcm4BsZjXH3fmzOXWB8qzYc3rmryMEXwNqtW3B6qR5yKyvqjh6JdUYmUQuWEL97LwmHjhK7aSsJ\nm7ehSktjynvvFcOrKjvDBg5Ed/4ixr9O8f6bxWTCnJbOqCFDcm3jq5kz0bzS7Ing6x9ya2sq9O3D\nio0befjwYbGNW1T6SnUGTPLoz+0lwA1BEH4ozb5FItEjSqWSFQsXMebNN7m+YDGyypWQ2dli0emw\n3LmHs1TGsmXLcHbO+7RaUTRs2JCDu3Zx9uzZR6WI2rYnICCA+Ph4YmJisLOz4/COHeJel1IikUjo\n2LEjHTt2LPa2BUEgMSERd6dH1QwUajU1Bg8kMzGJhJu3MBv0qPz9cRgcwL3ZPz33m9Jr1arF64F9\nWRy0BrfOHdF6/XPqVxcby8M9+7AbODjXuqAhISFcvn0L/3a5511TqK2xrlqZTVu25DqLJnr2lfYS\nZFNgCHBFIpFc/OuxDwRB2FXK4xCJXmiOjo4M6tuXL779lrADB7HI5UjMZhyt1fR/881SqcEokUho\n0KABDRpk3wB++PDh5zr4MplMHDlyhN/27iUlLQ0fLy/69OxJ1apVy3popU4ikaCx0WBITUX1xN4v\nKwd7PJo0evz/mQmJ2GiLZ4+OyWTi8OHD7Ny37/H7H9irV6kld3170iS8vbyYtWABDwQLCns7zOk6\n5KlpTBg6FC9Pz1zLLYWEhGDl5pZvXUqVhwe37t0rieGLSklpn4I8jlhwSyQqcz/Pm8dP69ZSrntn\nGlWo8HjWIT06hrlbt3Drzh2+/+abMqrJ93y7desWr0+YQLJCjlW1KsidHbgQGszaUa/TtHYdZn/3\nXZFPFD5vunfsxK4Ll/Bs2SLXe+IvXqJnp+wZ8gvr1q1bjHxjPClKZZb3f83IETSvW49ZM2aU+Psv\nkUjo06cPvXr14uLFiyQkJKDVaqlXrx4KhYLDhw/n+lyFQoFQgKTDZqMBhSL3gzSiZ5/46SoSvWBu\n3LjBTytX4j1kIHbe3lmWfDSu5fAZ2I+9F86zd+/eMhzl8ykiIoIBI0diblQfn6GDcKv/Es7VquLV\nsgX+48fwZ3wcYydOxPKvTOv/dcMGDSLz4iXSo3MulpL+MBr95asMHjCgSP2Eh4czYORILI0bZnv/\nK74xlj/jYxk/aVKpvf9SqZR69erx6quv0qhRo8fpP/JSs2ZNTDGxGFJT87zPcOcebZo3L66hisqA\nGICJRC+YlWvWoK5TC2UuR7Klcjl2TRqxKCioWPsVBIGzZ8/y/Q8/8Nn/vmTFypUkJCQUax9lbcGS\nJVC1Es41qme7JpFK8e7WmXP373H69OkyGF3ZqVixIjM+/oSotRuIOHESoy4DAKNOR8SxEzxct5GZ\nn3+Or69vkfpZuHQpVKuS6/tfoWtnzty7y9mzZ4vUT0mysbGhV5cuPDxyLNd7kh8Eo0hMLFBmftGz\nSwzARKIXzKETJ3CsUS3Pe5yqVObKtWvo9fpi6fP+/ft07NGDYe+9y6pb19kRE82Pu3fStH07Zsyc\n+Z+YEcrMzGTLzt9wyWFP298kUinqOrVYUQa1Dsta506d2LxsGa1s7Aj+eR63vvuB4J/n09rOgS0r\nVtA+l03pBZWRkcGWnb9RrsFLud7z+P1fu6ZIfZW0dydPxj0tnZAdO9Gn/DMTZjGZiL5wkfjtv/HT\nd9+XfJUKUYkqkzxgIpGoeJlMJpKTk1EoFGi12jxPkhmNxnw3+EqkUiQyGUajsVAJMcPCwtiwaROX\nbtxALpPxSuPGNGrUiCGjRyNtVB+/enWzjM2o07Fiw2YyMjP5ZPr0AvfzJL1eT0pKChqNpkz3VsXF\nxYFSicpWm+d92vJe3DmU++zGf1nVqlX5/uuv+eaLL9DpdGg0mgKX+MlPbGwsqKxQagvw/h8+Xix9\nlhRbW1vWrwxi5uzZbF6yDLmLM1KFgoyoaOpWrcrUhQupVatWWQ9TVERiACYSPcdiY2NZERTE6s2b\nyDSbMRuMVPL3Y/SQoXTp0iXHTfQBfn6EhIXj8u9s5E9IfxiNvdamwPm3LBYL337/PSs3b8KqejXU\nFcojmM2c372TyM8+xSYggBov1cv2PIVajXf/QNbNX8TQgQMLtQR169YtFi5bxq7f94NcjllvoHnj\nxowZPpyGDRsWuJ3iolQqMRuNCIKQZwBsNhiwzqcU1H+dXC7H1ta2WNtUKpWYDYb833+9AbUy/71Y\nZc3W1pbPPvqI9956iytXrmA0GvHx8SmVE8qi0iEGYCLRcyo4OJj+w4eTWcETl4H9sXZyRLBYSLx7\nl2k/zeXA0aP8OGNGtiBsxKBBvPPDTJyrVc21YHDsn6cZO2BggXMyzZw1i1UHf8d37Cjkf9VwBLBU\nqUxCORfiDx4i9tp1XKpnX/qUW1lhXbM6a9avZ/rUqQXq79ChQ0yYNg2rBvXwGT8Whdoas8HAlctX\nGfbWZKaNG8/QwYML1FZxcXFxwd3JmeTgEOx9fXK9L+XaTXq3eKXUxvWicHV1xc3RkZTgEOx8fXK9\nL+X6Dfq80rK0hlVkNjY2NGmSd21J0fNJ3AMmEj2HLBYLI8ePR6hflwodO2D9V5JLiVSKY6VK+A4d\nxO/Xr7F46dJsz23VqhVVnJwJ270X4V97rwRBIOrkKezjExjYv3+BxpKQkMDStWuoENg7S/AFPCrm\n7eyEY8f23N+7P8fM+wAab28uXb9eoP4iIyN5c9pUygX2wrPpyyjUj/qUKZW41a9HhaGD+GbeL5w/\nf75A7RUXiUTC6KFDiT9yDIvZnOM9urg49DdvEtinT6mO7UUgkUgYM2wYcUeP5/P+36ZvYGApj04k\nyk4MwESi59CJEyeIMRpwzWFZDx6dZHR5pTk/zJ3D9u3bOXPmzOON7gqFgqXz51NPY8Pdn+cTfugI\nMZcuE3H8BA8WLaVcRCTrlq/A3t6+QGP5dccOVBUroshpuVIiAQSsfLwxms2khobl2IZgMSOTF2wv\n0LoNG1BUrozW0yPH6yo7OzQNG7BoxfICtVdUgiBw9epVdu3ahZ2tLQ3LVyB47QbSo6P/ucdiIf7G\nTSJWr+d/H0zH3d29VMb2ogns04fmFQMIXrchS8oLwWIh7voNItas56vp03EVC1mLngHiEqRI9Bza\nuW8fqmo5Z1U3Gwzc272XhxcvglrNB8uXIk1Lx1YQePeNCfTs2ROtVsvS+Qu4efMmW7dvJzImBody\n7nQdNoL69esXqhzMvZBg5G7lcrymUqmQWAQwW1C4liMjPgFb7+x7WNJu3aFFi5YF6m/bnj04tG+T\n5z0udWpx4Me5mEwm5PkcOCiKkydP8vl3MwhLSEDl7oZgMJIZFoaniwsJGzYTq1Yjs7ZGHx9PpfLl\n+fa772jWrFmJjedFJ5PJ+OnHH1mybBmLg4KIVSmRWVuTGRdHFW8fvvvu+2KpbSkSFQcxABOJnkNJ\nyckotNlnnCwmE5eXr0SvUlHutaEIRiOubm7Y2NiQGhbOB7N+JCYujjGjRgFQpUoVphWxPIu1ygqz\n3pDjNYlEgqODA/FpqQhGA9IcZrkyEhIw3LlH4Oy5BeovLS0NF03eJWvkKhVIpWRmZmKTS76zotq/\nfz8TP/oIp47t8Auo+Hg/nSkjg6hjJ3AQ4PPp05HJZLi6uuLn51ci4xBlJZfLGTNqFCOHD+fatWvo\ndDrc3NyKnGNMJCpu4hKkSPQc8nRzQx+XPYlpxMlTZABOnTsg19pgMZlQ/DUDpC3vRYVB/Zm1eDHB\nwcHFNpaWzZtjvH0n1/1ddra2kJpG6rWbqJ9Y+hEEgeTgEMJXr+fTd98tcPHvci7OZMTF5XmPPjkZ\npUxWYmkp0tPTeeejj3Dv1xvHypWyHGaQW1tTvt2rJJRzYs+B32nSpMlzHXxlZmZy8eJFzpw5Q/QT\ny6rPOrlcTu3atWnSpIkYfImeSWIAJhI9h3r36EHmtWtZNtELFgvhp/7E9uXGSKRSzHo9SrkcldU/\n9eJUtrZY16zO6nXrim0sjRs3xkWhIO7K1SyPp6akcPfePe6FhJB07gJSBP78egaXfphD6LZfCV68\nDA4f44ePPqJv374F7m9wn0CSL1zM857Ys+fp0717idWy3LlzJxJPD2zy2Mvl1rwZW3fuIjWfkjLP\nKp1Ox4yZM2nUqhXDprzP6M8+5ZWuXRg5bhw3btwo6+GJRM89MQATiZ5D1apVo3GNmoTt2v04CDOk\npGLQ6x/tRTKbMSWn4Fou+94suyqVOXrqVLGNRSqVMu/HWeiPHifi2AlMmZnEx8cTGhmJ3mgk7cJF\nZMnJNP/iM+pNmoBUIaeKTMGyb2dwaNcuOnboUKj+unfrhiYhkZjzOQdhSfcfYLp6jRFDhxbHy8vR\n0T9PYVUx71ktpY0NChfn5zJY0el0DBw+nFV//oHrkIF4Dx9K+cED8H9zPJetlfQdPpxz586VWP8W\ni4XTp0+zdetWdu/e/Z8rWSUSgbgHTCQqkMjISEwmEy4uLlj/K9VCWZnz/feMmvAGV5YHoalXB9Vf\nGcBNqWlYMjJwK1cux2SXEpkMUy7H9J9WlSpV2LJqNT/MncuuWXOJMRiQ29hgSU3FvV5dfMZ0R6G2\nRunrg83okVxeHkRycvJTzVBptVpWLVrMkFGjCLl3D9s6tbFycsSQmkryxStIQkNZMmduiSasNJlM\nSK3yX96UyuWYTKYSG0dJ+XHOHO5jwbtn9ywHMmQKBe4NG5Do6MjYyZM5ceBAsYVL6asAACAASURB\nVJfD+W3nTr6e9SNJZjMSrRbBZML80Yd0aduOj6dNK1IC15s3b7J6w3qu3LiBXK6g1csvE9i7N+Vy\n+ENFJCppYgAmEuXCZDKxbv16dDod46ZNRa5UYsnIoGenzox9/XW8vLzKdHw2NjasWrKUY8eOsXzt\nWm6ePoeQmIgmIxM3Pz+UuZQQSg0O4eXKlYt9PD4+PsyZORPV1Kn8ducWrg0boHF3Q/avL2i5SvWo\n2PfKlbRpk/dpxtz4+fmxf8cOdu3axarNm4iJjcNWa8OQLl3p1bMnjo6OxfGSsrl+/TrHjh0j/uFD\n4owGnKpVRZpLKR2zwUBGVNRzt/9Lp9OxbttWPF4bmutpWIeK/gSfOs2BAwfo2LFjsfUdtHo1n876\nEaOdLckREcg0Gsx6PSq1mk1/nOT6sKFsCFpV6IMVJpOJDz/9hO0HD6KuXRObWjWwmM0s/uM4Py9b\nxqfvvluoZXCRqDiIAVgOLl++zMYNKzl39hgmkwn/ilXoEziCli1bFlvdMtGzzWQyMW7SRE4+eMDE\nocOoOPENJBIJhtRUdp05x67+/Vm7ZAmVixjI3Lx5k6C1a/j96DGMRiMV/fx4rX9/Xn311QLNLMhk\nMlq2bEnLli0B+Pb771lz+SLKqjmfbLSYTOguXmLYj7OKNO68HD9zBs+eXVHnsaneqVpVzu7c/ShR\n61POoKjVavr06UOfUkhqGh4ezqT33+NGaCjKgIoYrVREnjyJKcAfNy8vXFxcsj0n5vwFmtZvgJub\nW4mPrzhdvXoVmaMjKvvcS1UBqCoHsP/IkWILwGJiYvj4q/+RYDZjU60ybh3bI7O2QrBYyAwNI/nY\nCc7evcu8BQt47513CtX2l19/zc5Ll/AbOyrLHwQOFf3JaNyIT2bPws7evsgFwUWiwhD3gD1BEARm\nz/6eae/3p5LXERZ+70jQT250bxPMqmWTGTd2KDqdrqyHKSoFCxYt4o+wUPwGD0CmUj6eCVBqtXi1\nbolVy+a8PmFCkZaXFi5eTK/hw9kTE41tnx64DB1EuE95pvw8l75DhpCcnFzoNl8fPhybiCii/vgz\n26lEk15PyOattKr3EnXr1n3qcedHr9dnm/X6N6lcjlQmx2DIOX3FsyQmJoY+Q4YQ6uKM//gxVGjf\nFv+O7fFt24akQ0eJiojIdjow/sZNDKfPMuWtt8po1E9Pr9cjKUjwr1KRqdcXW7+rVq8mNjUVx26d\nsWvUEJn1o8MjEqkUax9vyvXvi1Gj5ueFCwv1cxMdHc26X3+lfO8eOf5cWjs64tK5I9/Onp3rSV6R\nqCSIAdgTNmxYx6njy1g9z59Bfcrj4WaNi7OKdq1cWfRDRbxcrvHRh4X7y0v0/DEajSxdvRq3tm1y\nrZXoXKM6yQo5R48efao+du7axY8rV1B++FA8X2mOtZMTKlstztWq4jN4IMHWKsZOmljoLwQnJyc2\nrFyJW2QU9+YtIuzQESL/PEPorj3c/2keXWrU4odvvy1UotXC8vPxIS0iMs97dLFxaDXqEksTUZzm\n/PIzej9v3Js0yvLz4Nv2Vbxq1SBhy3Zub9hE2PEThB07zoMly5H98SerFy4iICCgDEf+dMqXL09m\ndHSu5Xz+po+KonIxpnfYtH07Kn8/rH28c7wuVchxaPUKCelpPHjwoMDtbv/1V6yrVkL+xGngf7Pz\n9SFGl87ly5cLO2yR6KmJAdhfzGYzK5bN5uN3PLDVKrJdl0olTHnThyuXDhfql1/0/Ll69SomtTXq\nHJaVnqSqWpmd+/YVun1BEJg1bx4u7duistVmuy6RSCjf7lUu37vHlStXCt2+p6cnv27YyJo5cxhY\nqQod7R0Z16wFh37dwddffFHsm6b/bfiAAaSeO59n8Bh3+gzD+vYrsTQRxSUtLY1tu3bj2qRxtmsS\niQTfV9vQdMq72MoVON0PoU95H375+BMO79lLjRo1ymDERefj40ONigHEXcu9NqdJryfj2k169+pV\nbP1GxsaizmXp/G8qL08sCgVhYTmXtMrJg7Aw5Pn8LkskEhQuzkRG5v2Hg0hUnJ7tT79SdO7cOZzs\nM6hcMfsX4t8UCild2lqzc+evpTgyUWnT6XTI1PmfdFRYW5OSnlbo9m/dukVkchJ2frnPHkikUlQ1\nq7N5+/ZCtw+PvlDq1KnDu2+/TdeOHdFlZLBy1So2b95MWlrhx1wYbdu2xdvKmogDh3IMwqLPnccq\nPJJBAweW6DiKQ0hICDJ7O5R5bPpWaDRUaNsa53LlmD51Ks2bN3/mA8v8THvrLVIOHiE1PCLbNZNe\nT+jGLfTt0qVYD6Jo1NaQ3x5bi4BELi9wnVIAjbU15ozMfO8T9Aas8pglE4mK2/P9KVGM4uPj8fLI\n/0yCl4eS+LioUhiRqKy4ubmRGRufJclpTvSxsfh4Fv4LKD4+HqWDQ77LgFaOjkTFxOR5T15u3bpF\nu65dGTF1CiuuXmZ98H0+X7uaxm1as3jp0hLb76JUKlmxcBH+GXruL1hM5Ik/iL95i6gzZwleHoTm\n2k3WLVuGk5NTifRfnCQSSb4/BwCCRUAiLbll3dJWr1495s+YQcKmrYRs3EzM5SvE37hJ2P4DPPhl\nIT0bNOTjDz4o1j4b1q2H4eFDsOT+c6lPSsLaYsHHx6fA7b7aqhWGm7fy/Hk3pKZiinpI/fr1CzNk\nkahIxFOQf9FqtcQl5J8bKS7BiNa2ZI64i54N/v7+VPT0IP7WbZxyO01oNqO7co3Ad95//JjBYECn\n02FjY5NnAWitVoupALNQhtQ0HAvxl/6T7t+/z4CRI1C1aIZvzRpZgr3MpCRmBq3EaDQybsyYp2o/\nP46OjmxYtYoLFy6wcetWIqNicLSzo/vUaTRv3vy5OU3s6+sLaelkJiVhlce/Rfrdu7zcsEkpjqzk\ntWjRgj8OHmTnzp38fuwoBoORKlWr0//jT/H2znmfVlGMHTmSvWNGk1mjOionx2z7L03pOjKv36R1\ns+YFLlsF0LBhQ9zVGmIvXqJc3TrZrguCQNTBw/Tu2hWtNvcVEJGouIkB2F8aNGjApx9LCI/MwMsj\n5+Uni0Xgt/2ZfPVtp1Ienai0vT9xEqPeew9rF2fwzJrQU7BYCP31N1rWb0ClSpW4cOECi1Ys58CR\no0jkMqQCdO/YkZHDhlGxYsVsbdeoUQMbIDUiEq2nR479C4JA5rXrdPv8i6ca/7c//oi0Xh1catXM\nds3K3h7vgf2Ys3Axgb17F+rLrDAkEgn16tWjXr16JdJ+abC2tqZfjx5sOH4S7y45/97rk5PJvHmb\nft//WMqjK3lqtZrAwEACAwNLvK8GDRrQvGZNTl+4hL5WDaRWVkjkMgSLgJCph6QkbG7fZdrSpYVq\nVyqVsmDOHPq+NoywhERcGzV4vKScHh1DzNFjBCitmFLI1BYiUVGJS5B/UalU9OrzGt/9HIHRmPOS\nw/J14Ti5VKN69eqlPDpRaWvWrBlfTZlC5Mo1GJOTSX4QTGpEJFF/nuHBoqXUd3Bi5jffsGbdOga9\nMZ4zEvCfPIFK70ymwthR7IuLoceQwRw7dixb21KplLGvDSdm3++YczlOH336LJ4aDY0bZ9/8nZ+Y\nmBiOnDqFa/2Xcr1HqdWiqlSRzVu3Frr9F82EceNwSUwm/MDBbP9eaVFRhK5ex/tvTBCzqReRVCpl\n4U8/U1+jxerEKZShYagSkrCKjUN15RrWf5xm3owZ1K5du9Bt+/n58eu69XTy8CRs4VKCFy3l/ryF\npGzexpg2bVm9dOlzcSJX9N8izoA9YfToN5g29Q5j3j3Ma/0cadbYCalUws07qazdEsu1O07MX/hz\niR7hFz07evbowctNmnDk6FFsL1zCYDDS2N+foTO+o379+ly+fJkvZ8/Ga8hArBwdHj9PaaPB85Xm\npPr7Mf7999i/dVu2ZJxDBg3i1p3bbFsehN3LjXGqWgWpTEZ6dAzxp89gEx3L4mXLnmoz9927d7HO\nIQP9v1l7V+Ditat53iMCOzs7NgQFMf2zTzk0dx5W/r5IlErMsXFYZWTw5eS3ivU04IvMzs6O9UFB\nnDx5kqD16wm+eQcrKxVdOnaid69eRapw4OHhwf8++5wP3p9CREQEcrmcChUq5LldQCQqSeJP3hPk\ncjnfzpjD7t27Wb5+EdP+dxW5TIKdvTO9+kzgvY/6FqkOWVlKSkpi0+bNBG3aSPTDh1ir1XR69VWG\nDRpMpUqVynp4zyxXV1fKubiwY8PGbNcWLV+OplH9LMHXk7ReniRVCmDDxo1MfPPNLNekUin/++xz\nWv3+O4uDgji3YydSqQx7Wy2j+g9gYP/+ODjk3G5+ZDIZFGDjuMViQSZ9PvZilTVHR0fmzZ7Dw4cP\nOXnyJHq9Hk9PT15++WXxC7yYSaVSmjVrRrNmzUqkfY1GI37miZ4J4ifHv0ilUjp37kznzp3R6/WY\nzebHxZevXLnCtm3reBgVgkajpVXrbgUuGVOW7t+/z8CRI8l0K4dDm1b4l3PBpMtgz6VLbB06hE/f\neZe+pbDH47/EbDaz/9Ah/CdPyPM+hzq12LRzZ7YADB7tkWrbti1t27bFYDBgNBpRq9VFnmGtUqUK\nhpgYjOnpKDSaXO/T37tP097iv3thuLm50Uuc7RKJRMVA3AOWB5VKhVqtJj09nQlvDOeT6QPxdtnP\nwK7htKx/md3bP6B71xZPlSyztGRmZjJk9Cho+BIVundF6+WJTKlEZW+H5yst8Bw6iE9+/IHTp0+X\n9VCfKxkZGQhSaZ7ZtQGUNjakpqbm255SqUSj0RTL8radnR1d2rbj4Yk/cr0nPToGc2gYXbt0KXJ/\nIpFIJCo8cQYsHxaLhbffGoO363VmfxqA9IlcPx1fheOn4nh78lAWL91WLEez09LS+O23HezZtY6k\npHjs7Bxo16EfXbt2e6rlz71795Jmo8E7h+PX8KgOmm2zl5m3ZAkNGzYs6vBfGGq1GoVMij4lBVUe\n/y4ZcfGUyycLd0l4/+23+WNAf8IPHsa92cuP94MJgkBycAixO3by3cefYJNHglFR4aWmpvLrjh2s\n27aNxKREHB0c6d+jB127dBFTHIhEoizEGbB8nDp1itSky0yZ6JMl+Ppbs8bO9OsuY/nyBUXu6+bN\nmwT2bsOl0zMYOziZWZ/bMH5oGtcvzCSwdxuuXbtW6DbXbtuKJodUBE9yrlmDk2fPkpSU9LRDf+FI\npVJ6d+1G7Nnzed6XfPESg/v0KaVR/cPJyYlNq1bTQGXNvbnzCNu6nfAduwhevAzp0RP89MWXdOnc\nudTH9V92/fp12nTpzIytW0iqVR2rbp1JrFmNGVs20aZLF27cuFHWQxSJRM8QcQYsH1u3rCKwqybH\n4OtvPTu50XvEdt5778OnPsqckJDA5IlDeXecitbNPR8/XsFLTYO6Dhw9Gcdbk4ayas3uQrUbF5+A\nVa2802bIFAqUNhqSk5MLVeLjRTdi6FC2DuhPsr8vdjnMfsZevoIqOpbu3bqVweigXLlyLJg7l6io\nKM6cOYPJZKJChQrUq1fvuSiVk5aWxunTp0lPT8fV1ZX69es/s+OOjY1l6JgxKFu1wK1a1cePq52d\ncajoT9zVawwZM5q9W7c9FxUARCJRyRMDsHxEhN+jap+8lw4c7JXY20mJi4ujQoUKed6bm02b1tO8\noZHWzXMubdPiZWdOX0hj48Z1VK9eq8DtOjrYE5GUjI27e673WEwmDOnpz+0Jz4JKSUkhNTUVe3t7\nNBoNYWFhbN68nps3ziKRSKhRswm9e/fNljIiNz4+Piz6cRZj3nqLZH9fHOrURqm1ISM+geQLl7CO\niydo4cIyf1/d3d3pVkZB4NPIzMwk6uFDGrdpjdzNDam1Fcb4BGwFgXffmEDPnj3LeojZrN+wAbNv\nBZyfCL6e5FyjOqHBoazfuJHxY8eW8uhEItGzSAzA8qFUqkjPp+CyIAjodKYinYb87dfVfPth3hnJ\ne3V2YeKHqwsVgPXr1p3PVwflWlIHIPbqNRrUrv3UaQ+edSdPnuSXJYs5c/EScmtrTLp03B1sMWeG\n06eLPcN6aREEOHlmBQP7zWPIa+8wfPjrBWq7cePG/P7rr2zcvJnNO38jISUFZydnRvfuTfdu3cR9\nP4VkMBgYMXYszVo0x3PkcFS2/7x/qWHhfDDrR2Li4hgzalQZjjK7VZs34dg97wMNji/VZdUmMQAT\niUSPiAFYPpo07cDvRxdTrbKWPQej2bEnnIcxmaitZbzysiu9unoSFZ2JvYMXrq6uT91PbGwsPuVz\nD5IAfCqoiY29W6h2O3bsyHc//UTslau41KyR7bo+KZmUYyd44/uZhWr3ebF46VJmLl2CXbOmBLz1\nJlK5nLAD+5E82MM3H9pRrbI9drZ2ADSu78iQQD1vTP0BGxsbAgP7F6gPFxcXxo8dK36xFoM1a9Zw\nJTGe1vb2qAwZWa5py3uhHNSfWYsX075t20IVZC5JgiAQFxuHSz6HLdQuzoQVobh6WbNYLBw/fpxl\na9Zw/dYt5HI5LRo3ZujAgVStmvPMn0gkyt2zuaGijAmCgMlkAqBXr0B27E2n97ATHD3xgBH9VSz5\nwYUvp9hjMsQzZOwpPvr6PoH9RhUphYBGoyYxyZjnPYlJhsc5yQpKrVazcsECTMdOEvrbLtKjoxEs\nFozp6USe+IOwFav4YPwbNGny3yokDHD27Fl+WLqECkMHU65OLaRyOSa9nrSzh/nycz+cvJ0Jj4zE\nYPynvIyLs4qvp3uxeOH3GI15/3sUhSAIGI1GBEEosT6eNxaLhcWrV+PcrCnk8ruksrXFqkY11q5f\nXyx9Pvm7/rQkEgnWamsMael53mdMT0edR162Z1lGRgYjxo5l/Befc93OBrvAXlh368y++Fh6jRzB\nrLlzxZ9lkaiQxBmwJ5w5c4Z1a5dw4vhBLBYzTk7OdOoyAKlMRatmckYNdkRrI0cqAbdyUKG8grq1\nlLz9aRoBAUXLrNyqTVd+27+L1wfnvofst/0xtH618HmbKlWqxO4tW1i3YQNBGzcQHBuHSqWiY9tX\neW3hQmrWzPuU5PNq0YoV2DRqkGUZK+7KNRrUVuDi8mi5WGJlRUJCAm6u/+z78ve1wdszmuPHj9Oq\nVatiHdP9+/dZvmoVW3b8SkamHmsrFb26duO1wYPx8/Mr1r6eNzExMcSnpVLRyzPP++yrVObIyVNM\nK0Jfly5dYsnKlew7eACj0YS9gz2Devdh8MCBT1XTsUu79uy7cBHPV5rnek/cxUt07dChCKMuO1M+\n+pDzSQn4Dh+K5ImDEGqXZhhfqsuCVWtxd3WlX9++ZThKkej5Is6A/WXBgp/4/JNhNKl1gd83VeGP\n3bWY86Ud5/+Yi4M2nNeHVCUpRcndB5kEhxu4F6InIspCjWrlmf6WH0Er5xeoH0EQePjwIcHBwaSl\n/bO3rF+/oWzakUFouC7H54VHZrBuq45+/YY91etzdnZmwvjx/HnoMHcuX+b6uXPM/Obb/2zwZTKZ\nOHT0KC61s+6Xy0yIp3rAPz/2crU1Sckp2Z5f2V9GREREsY7p0KFDdBs0kJ0RoXi+Ppzq06fgOWok\nOyPC6DZwIAcOHCjW/p43FosFqUye70yyRC7DZDY/dT8rgoLoP24sf5gM+E18g2rTp+DQtw8rL5yj\nQ69eXL9+vdBtvjZ4MBkXLpIRH5/jdV1cHBkXLjN0wMCnHndZCQ0NZf/x41To1iVL8PU3hUaDW5dO\nzJo/H0sBSmCJRKJHxBkwYP/+/ezd+QvL5/jhYP/PRnp/Xxs0ajPd2mmJi4vG378SRpMJk9GEVCrB\nysoKkNChtYm5iw+TkpKS64k3i8XCtm3b2LBuAQnxoWg0chISTTRv0ZnhI8ZRsWJFJkz6ijHvTuP1\nQVo6tnFFrZaj05nYczCaJWtSGT3uM6pWrUp0dHSRXu+zepS/OGVmZoJMlq0gtVShJDX9n6USiVSa\n45dGmg4qqFTFNp7Q0FDenDYNl8CeaD3/meFR2WrxbPUKaZUrMenD6fzm7//M7G0qbc7OzsjNZjIT\nEsE993QuKcEhNKtc+an6OHnyJN/Mn0eFYYNR2dk9flzt4kyFju2Ju36D18aN49CuXWgKsVxYuXJl\nvnx/CtO/m4FNk0a41K6FXKXCpNcTe/Ey6af+5KupU5/LGoTbd+zAqmoVpHnUvNR6ehAvl3H27Fkx\nobNIVEBiAAasWvkTk0c7k5RsZPHK+xw7FUum3oyHmzURUTrGDyuHUmEhJTUVO1s7lIqsX+pqtRxH\nRyWJiYk5BmAWi4VPPplC6L3dTH7dmQZ1qyCRSEhJNbJ9zxHGvL6Pb79fRrdu3fH29mFV0ELmLD6A\njUZGWrqZBg1f4X/fjKFevXql9ZY899RqNVYKBZlJSVg9kdvMsUol9m7aw7ChAjKZBIvRhEKR9ddA\nrzdz7FQGo95sWmzjCVqzBmXNalmCryfZeLiTVKM6QWvW8NEHHxRbv88TpVLJgF69WHvqT+iZc71F\ni8mE7sJlhs6a9VR9zFu6BLvmzbIEX09yrlaVkGs32LVrF4GFrI/aq1cvfH19WbBsKYdm/4zMSoU5\nU0/r5s0YM28+derkXI3iWRcZHY3cIf/8gHIHe+Li4kphRCLRf8MLH4BFRkbyMOo20TFaPv/uCr07\n2zD3f05obaTcuqfn7U8SuXozldbN7UhJTnx8Yu5JZrNAcrIh17IuGzduIPzBbuZ/549KJXv8uK1W\nwZDA8lQNSGTq+6PZvuMYtWvXpnbtn9HpdKSmpqLVap86ueuLTCqV0q9nTzafPY/Xq60fP27j7k6U\nxovfdsbRvZsL5owMXBwdszx3+boIatZujoeHR7GNZ8tvv+E8sF+e9zjXrcOW1Wtf2AAMYNSIEezo\n2xdjWjqCTMiy5GXS6wndsp029etTt27dQredlJTE6YsXCZicvTD6k7S1a7B++/ZCB2AAdevWZX7d\nuf+p318HW1tM0ZH53mdJ14mlrUSiQvjvr0XlIykpCUEwsXT1HZb+6MaYoQ54l1fi6CCnSX0Nk0Y5\nceSPDOIT9JjMOZ+WOnIyDh+/6jlmuBYEgfVrFzBhRLkswdeT6tdxoE51Mzt37nz8mFqtxtXV9bn/\n8C5Lrw0ZguXGTRJu38nyePkeA1mw3sTihcEkx+mx/2s2JDomk+/m3mffUVs+/OjrYh1LSkoyStu8\nc4Kp7O1ITUl9oU+TOTk5sWHlShRGI/fmLybs0BEi/zxN6M7d3P9pPt1q12HmN9881YnjlJQUFGp1\nnktpACpbOxKLWJbrv/T726FdO/TXbyLksb8rMyERS1y8uPwoEhXCCx+AOTo6EhoWy8RR9nh5KLJd\n7/yqLbfvGbl8IwOLJfsXY3KKkV+WxTN4yBs5th8SEoJBH0OdmjkvefytYxstRw7veLoXIcqRp6cn\nK36ZR8a+A4Rs2Ubi3XukR8eQHh2NysmX7TtlTPlSYNibIQwad49B48ORaPqwdPnmYi8X4+DoSGZi\n3l/qGQkJ2DvYFymdyX+Bp6cnFf38WDt3LgMrVaGjvRPjW7Tk8I4dfPX550+d8Nje3h6TTofZYMjz\nvszERFycxXJBf6tZsyZVvMrz8MQfOV63mM1E7dvP0H79/toXKxKJCuKFX4KUSqUoFRLq1875g0Nr\nI+ObD90Z/W4Y3TrIGPOannIuKgwGC78fiWHxmiTadhhN69atc3x+RkYGtlpFvl+qtjYKdLrUIr8e\nUVa1a9fm0K5d/LpjBxt37CA5JRlPFxemjHuDdu3aYTabCQkJAcDX17fQedYKql/3Hqw6fx51+3a5\n3hN//iKDejx7ZXbKyqPl+NrF1p6trS3NGjXi8uUruNV/Kdf70i5dYeCIkcXW7/NOIpEwb9Ys+g0b\nRnB8Ai5NGqJxdUWwWEi6d5/Ek6do4uvHpAkTynqoItFz5YUPwOLi4vD3cyEhyYytVo5Cnj1Q8i4v\nZ9xwVxavUXPoj1CkEiOZegt16zXm3SmjadasWa7tlytXjofRejIzzVhZ5bwECXA/JB03t4KXGBIV\nnK2tLYMHDWLwoEE5Xq9WrVqJj2FAv36s3LiRpIAA7P18s11PehCM+cYtBn75VYmP5UU2fuTrDHpj\nPLY+3qids5f+ijl/AW16Ou3a5R4ov4hcXV3Zvn49q9euZcW6tUSkp2MxmfH39eGtUaPp3r07Mlnu\nn28ikSi7Fz4As7W1JSNTjoODMw9CH+JoL8NWK0cmg0y9hcQkM5l6Ge5ubjRsVI0fflxEamoq1tbW\nWabbdTodRqMRrVabJc2Dk5MTNWu/zN5D1+jeMedN3RaLwJZdOt5+/9nOEWQwGNDpdGg0GhSK7Mu1\nhXH37l22bdtAeNgdVCoNzVt0oG3btqiKMfXDs8TDw4PFs2czavIkUv39cKhbBysHe/RJySScv4jl\nzl0Wz55drBv/RdnVq1ePr6dM5YNvvsaqZg2c6tRGoVGji44h6fwF1HHxBC1eIi6l5cDOzo7xY8cy\ndvRoUlNTkclkaDSaF37JXCR6Wi98AObp6Ymziy+376dRr1ZFEhPjCQ5LRhAEFAoF9vauuHvaM3dZ\nCB269UEulz8uWi0IAnv37mX9uoXcvnUFpUKGXKGmW48hDBgwBOe//sIe+fok3n1rAJUrplIlIOtG\nbItFYPaCEDS21ahfv36pv/6CuHDhAguXL+Pg0WNI5DKkAnTr0IGRw4YREBBQqLYMBgOffjKFC+f2\n0r2Dmh5t1KSlm9i74zhzZn3GNzMW/GfTbTRo0IC9W7ayfsMG1v+6neikJOzt7RnerTt9Z3yHm5tb\n/o2IiqxHjx7UqlWLoLVr+W39JnQZOtzd3HmrTx969uyZay4/0SNSqRS7XNJ4iESignvhAzCJRMKg\nIROYvfAdFv1gi7u7J+7uWXM17T8cw70QNW3btn38mMVi4dNPp3Lv1i5eH+hIs8Y1kMkkhIbr2LAt\niKGDNzBvwTq8vb2pVasWU6fPZcK0SbR8OZ72rezQ2si5fS+NTTvSUFhXHZWxaAAAIABJREFUYdbs\nhc9kgtS169fzxexZaBo3xH/yBOQqFcb0dPafv8BvQ4bwy4wZtGjRosDtffThu1gyD7N1eSWUyn9e\nb6e2cPp8Au+/8xq/LNj0XCasLAhXV1cmvvkmE9/MOxWCqGT5+fnxyfTpfDJ9elkPRSQSvaBe+AAM\noEOHDty5c53hE5cyYoAdbVuWQ6mUEhahY9OvMew7KmXuz2uynL5asyaIiOBdLJrpn2VvVwUvNe9O\n8KFSxSjemjSCTVv2I5VKad26NXXqHGHbti3MX/0b+swMPDxrM27iEJo0afJMBl+XL1/mi9mz8Ro8\nECtHh8ePKzQaPJs3I9XXlzemvM++LVtxd3fPt73r169z7crvbFqSNfj6W8N6jrw+SMeihbP47vtf\nivW1iEQikUj0LBEDMB7Ngk2c+A4vvdSYdWsX879Zx1HIJaisNHTtPpig1UOyFOi1WCysW7OAGR+5\n57qxvlsHd7buusuJEydo3vxRgV5HR0dGjHidESNeL5XXVVSLV6xA0/ClLMHXk7ReniRVrsT6jRuZ\nPHFivu1t3bqWnp00OQZff+vSzo2FQYdJSEj4f3v3Hd5U1Qdw/HuS7j2BDqDsIRtkT1myNyKC7OUA\nRFQciIior4gMRQRRQEBZKggioiLIEpAhiKJsKN17N2ly3j9uit0tUtIWzud58pTknpx77skt+fVM\nvHIskKooiqIo9woVgGXRpk0b2rRpg9FoxGAw4OjomGfL1Llz53BxSqJ2jYLH7PTu6sie77ffCsDK\nEpPJxPc//US16QVPLfds2IAvd+4sUgB2/do/dB5c8P56Tk42+FewYdmyZVy+eRNDhpEGtevw6NCh\nVKpU6bauQVEURVFKq9LX71UK2Nra4uzsnG+3YGJiIl6ehc8C9PayIykptriLZxVpaWlIIbApZDaY\nnasLiUlJRcrTzs6elFRTgWni4uP4+8I1Nhw5zN/lvLlWKYBN5/+k+9AhzHvzzTw3zlYURVGUska1\ngP0Hvr6+3LiZhtks0enyn4J9/WYqPr55b75c2jk6OmJna0N6fHy+GxcDpEZFU84393pKeWnZqhs/\n/vIuHdv45nk8MTGRw8evESM9qfPYMHSWdYW8atYko21rNm7cgp2dHS/MnHn7F3SfiYyMZMuXX7J9\n926SkpMJ8PNj5JAhdOvW7Z5d6kNRFKUsUS1g/0H16tVxdavEsZP5t26ZzZJt36XSp89gK5as+Oh0\nOgb37UfkiVMFpos/dZoRg4u2aXGfPn359YSZv/5JyOOo5GZoKOt3GHBr1ulW8JXJxsGBSkMHs3bz\nJqKjo4t6Gf/mfh/tr/jLL7/wUJ8+rDx4gPRWzXHs14vgoIq8vHIFvQYOJDQ0tKSLqCiKct+zagAm\nhPhUCBEhhPjDmuctbkIIxoybwdvvhxMRmZ7ruJTa2l7l/RpTv379Eihh8RgzciTGs38Qf+Vqnscj\nz5zFPjyS/v36FSk/Nzc3Zs9ZwjOzQ/nuxzCMxn+7E/+5GMO898I4HVmJgA4d8ny/rZMjdjWqs337\n9iKdLzQ0lCVLFtK964M82LQ6Hds3YN68V7hw4ULhby6j/vrrL6Y8/zw+gwdQqXcP3CpXwsnHB5+6\ndQh6bBjxVYN4fMIEDIXsh6goiqLcXdbuglwDfAB8ZuXzFruuXbsSFvYCjz/1DgN7OdGlvTdOjnr+\nOJ/A5m8SMJqrs/SDZWV6lejKlSvzyZKlTJg+jfgqQXg0aoC9qxupMTHEn/odx6ho1q1ceVsLV3bq\n1Al393Ws+GgBSz4+TdUgR5KSTVy8nEI4gTwwdQI6m/xvS9vy5bho2buxIKdOneL5mWPp0UnHigW+\nBPoHEh1jYMee73ly8tdMm/E/evXqXeRylxXLV63CsUUzXAPz7vr2a9OKq1eu8tNPP9GjRw8rl05R\nFEXJZNUATEr5ixAiyJrnvJtGjhxN69bt2Lx5PTNf/xGDwUClytUY+thoOnXqdMfb9fxXUkpOnz7N\niRMnMBoNVK4chNls5saN69jZ2dOiRQseeOCBIgWHzZs356dvdrD1q6/YumMHsYmJ+Hh7M2nQIPr2\n6YOrq2uheeTUpEkTVqz8guDgYEJCQrCzsyM8PJxZHy0vMPgCyEhPx9Gn4DFMMTExPD9zHK8/706L\npv8uZeHrY8/Y4RV5qG0yk597nipVqlplH0hrSU5OZs++fVR9ekqB6ZwbNWD91q0qAFMURSlBwtpj\nYywB2E4pZb0C0kwEJgKUL1++6caNG61TuDIiKSkJFxeXPI+lpaUREnIDKY24OgukNJOYZCTdIHFz\nscXeXk9ikhmd3p6AgErZFpctSSaTifP//IOdry9Cn0/PuARDVBSVAwJwds5/OYuoqCiM6ZH4lc//\n2mLijKSlu+AfEFho2Qqq79LEaDRy4fJl7MrlPckhk9lohIREalavbqWS3b6yUuf3ClXf1qXq2/qs\nWeedOnU6IaUsdG/BUhmAZdWsWTP522+/3dUylTX79u2jY8eOuV7/559/eHLKUJ6d7EzXjuWIjY0h\nJiaUiv52XLthZObcSMaPrEnv7n7s3BPGh2sMrPr061KzvtaLs2fz3dXLVOz5cJ6tc1Fn/8D+5Gl+\n+nZXgTsHDB3chZenSurXzX/2ZkKikV7DL7D/wB/YFNLqll99lzaxsbG07NqFGs9MzTWJIau4S5fx\nPHuO7Rs3WbF0t6es1Pm9QtW3dan6tj5r1rkQokgBmJoFeQ9Z9N7rTBppT7dO5TGbTURGhlEpwB57\nOx01q9mz5I1yLF3xN2lpJvo+7MeIQTreX/p2SRf7lhefe46A5BSubd9BWsy/M0wz0tIIPnCQtP0H\n+GjxkkK3bYqPj6VCuYLXL3NztcXWRpKSklIsZS8NPD09qV+7DjF/nS8wXcLZPxjwsOp+VBRFKUkq\nALtHXL9+nUsXTtC7m7YnY1xcHK4uAjvbf1uSqlSyo3F9e3b/FA7AwF5+nDj+MxERESVS5pzc3NzY\n9Nk6hjdpRvi6z7n26Vqur13PlWUraOfowlfrN1CrVq1C8/H09CY0PK3ANPEJRjJMOpycnIqr+KXC\nE2PHEvvLQYz5BJZxV67C9WD69+9v3YIpiqIo2Vh1EL4Q4gugI+AjhAgG5kgpP7FmGe5V58+fp3F9\np1v7LKalpeDilDu+btHUnr8vJgABODnZ8EBtJy5cuJBtr8uScP36dX744QcSE+MI9Pdn5+bNxMXF\nYTKZqFSp0m3tC9m9xyNs372MBg/k3wW54/twOj3Uq9Dux7LmoYceYuIff7ByzTrc27bGp24ddDY2\nGJKSiDxxCsPp3/lkyVI8PDxKuqiKoij3NWvPgnzUmue715hMJvbt28fNm9fp1uVZdDodjZu0ZsjQ\nUUgpyTWcL4/hfWazzPd5Zv5bt3zKpYvns+XfuHHju7KkRkJCAnNencm5swfo1sEBby8dV/8y8+nH\nb9Kxc39mzXrtticK9O8/kEeGfMjBX6No2zL3Kv0XLyexfmsyS5eVjU3Rb9czU6fSpGFDPlqzmhO7\n92Bjbw9GI/169GTChs+pWrVqSRdRURTlvndv/fl/D0tJSeHZGZNJSTjFoCFPseHDChiNkv1HfuW1\n2T/SoHFvTp5JIT3dhL29HkdHZ5JSknDPsUTX4ePpPNRBWyMqKSmDP/9Oo3bt2rfyT008xbD+bjSd\nkT3/dh2HM3PmS8UahKWmpvLE5BE0rhPMW+tq3Wq9A5g2MYN5C3fy/HNRvLfoo0LHfWXl6enJwkVr\nePaZ0XRum8yAnt5UDHAkOtbAN7sj+XpXGjNfWEjt2rWL5TrMZjOpqak4ODigL2DwuzV16NCBDh06\nkJSUREpKCh4eHqVmxquiKIqixoCVGa/PnUU59zN8srg6bq42eHvZU6G8A4/0D2D9smpcu7gTewcf\nvvpW22bG3cODpGRJetbV5i+lc+68kW4dte7GTdtDaNGqC97e3rfyX7WoOt06lc+V/5kTn7Nu3Zpi\nvaavvvqS8l7XmD65crbgC8DZ2YY3XqpKROhhDh48eNt5169fnw1f7Mat/BienZvEQwPPM3Z6BImm\nfqz8ZAfduz98x+W/evUq8+e/Ssf29Xm4a2PatanLrBemcubMmTvOu7i4uLhQrlw5FXwpiqKUMioA\nKwNu3LjBieM/8OK0oDw3/3ZxsWHOzEASE+NYsymDr74NAamjfHl/rgcbSE0zc+psKtNnR/Dc03XQ\n6wWffxnMV7tsmDptVpHz37BuGUajsViuSUrJl1tWMXKIT76tajY2Oh7t78aWzav/0zl8fX2ZMuUp\ndnx7mCNH/2bPjyd44YXZVKlSpdD3JiQksH79OsaNHcSVyxeYPm08e/fuJSMjA4AjR44wfkwfvB13\nsWVVEPu/qcfujbVoWOMoL8wcxpYtpXeJB0VRFKXkqS7IMmDXrp083MkxVytRVlWDnKlRVU/33rP4\ndtdmPtnwJx1aOWA06Pj54E3CIkx0aF2OE2dSeWvpH6D3on279uzY8Q1nfv+d1k0NxMSGY2dnj7u7\nO3qdPlf+gX7hHDt2jDZt2tzxNaWlpREWdpP6dQteDq55E08+WG3dFqVjx47x0qxJtGoK44a6k2AC\n35Z/sn71dFatrMQrr77D7Jcns2BOORrW+3egv4uLDY/0D6Bdy1QmzJhLzZq1adiwoVXLriiKopQN\nKgArA6Kjw6jqV/hHFeinx97enieefIGPVy5myzeHtVmElRsyqncP3N3d+X731wiRQJ8uGXh77uGv\nP8LZ+2MsVSrbMjpNj8moIzIiFG/vcvj4+AAiW/7R0dHFck06ne7WxIGChpWZTPK2xn/dqUuXLvHS\nC+N4+xVfmjTUZgr+clpH+64V6NFFsmr9DSaMf4ReXWyzBV9Z+VdwZNQjrny+YRUNG75vtbIriqIo\nZYfqgiwD3Ny8iI7NKDRdZLSJ777bzvzXR9Ol1UV2b6rLvu0NmTHBzIVz6/hw2Vs0rhPG7k31eGKc\nHy2bpDFrqiffb6pEw7p2zF0Qia+XDVUr25GQEEFkZGSO/M3/ae/HvNjb21OlSg2OnYwtMN2BX6Op\nV795sZyzKNasXs6IIfa3gq+shBCMH1ERT5cQfL0K3kGiV5fyHPhlT7F12SqKoij3FhWAlQFdunTn\n2x/TMJny/9IPC0/jwJFokuN+5bP3qzG4bwDeXva4udrSvrUPfbq5UqdaAiMH67Cz0xEZEYa3l8Dd\n1QZvLztGDXXF2RF2/ZSIrY2gUoAdMTERGDO0ACI0LI3zF820bNmy2K5r0JDxrNkYnWtpjEwpKRls\n3JbE0EdGF9s5C5KSksIv+3fR72G/fNMIIRjQw4mjJ6IKzMvZ2QY7W22mp6IoiqLkpAKwMqB27dpU\nrNyYj9fdyPN4RoaZt5fewNZWx6vPBuLiYoPBYObvi4mcO59AQqKRr3Ze54kxXqSnJ5OcnExyciIe\nbrYAONrrsLe3oWcXJ77cGQ+AjV7g7qojLi6WjAwzC5YF02/ACBwdHbOd22w2c/jwYWY+O4Whgzsz\nfFh3Fi9+l+DgYABu3rzJkiULGT6sO0MHd2bGMxM5dOgQZrOZvn37ondswuy3rhAbZ8iWb2hYGs+8\neplGzfrRrFmhW2oVi9jYWFxddLhb6iU/QZUdCQ4peAujmFgDZmlT4KbhiqIoyv1LjQErI958aylT\nJj3GjZuXaN/ZdGv81KGj0azZFEOqsQb1617Cr7wDH3x8kW92B+PlIbCz0xEcYiQ0PJ1F86pgSDcT\nGxuDg4MOvU5bqzUpOQNbWx0BfjYcPJbM4eNJtGrmjIODYO/BSL7dG4eHT1umTJnGsWPHOHDgZ9LS\nkvDxCeDY0X2kJJ5jcG9nJg1zIy3dxN4DXzBqxKc0atqN0yd+oHdXB2Y96Ymjg54/zp9h2ZLJrPus\nEQvf+4jFi1eyaNHbDB63hWYN7fDxEgSHmvnzHzNDh01mwoQn7soCsHlxdHQkOdmI2SzznA16i3Ah\nLj4y/+PAtu/C6dKtf6lZF0xRFEUpXVQAVkZ4e3uzeu2XbN26hZth6bTr8wdms6RmzboMHfY8APu+\nf4VJM05QpZKJVQvLUSlQW/spIdFEu36XuHI1Gb8K9mRkGBFAapqZm6Ep6PXg6qLDx1uPrY1g9NRg\ndDo9DvYCe8fyzJmrLVo6YngfMN+ke0d7XD1t+Gj1FaoFmXhndg38/f0QlgH7D9R2o/tDUYyYtIqZ\nT9WhW6fynDwTj9FopmY1F9a+X4G3lpzlpZemsWTJKmbNmsMTTzzDgQMHSExMpEkbbxa0a4eDQ8Eb\nahc3Ly8vgqrU5eCv0bRvnXsF/UyHjplJTffgh30RdO2Yewunc+cT2Ph1KitWjb2bxVUURVHKMBWA\nlSHOzs6MGjWaffv28dPPZ9Dr9bcW2Dx06BCHj4bRs7Pgxam+t1qNTGYz9vYZtG3uwMWrBuztBWaz\nNqA/LT0dv/I2uLloPdF79qXRpb0Lr79QgWfnRBARbceo8W/QpEkTxozqx5NjbOnVtQZCCP65lIi9\nnZGl8wMIi4wlLFTi5xdgKanEVhfL/Jd8eOWt83z06T80qu+Ao4OOc3+n4+riwJSxNXhr6WH++usv\n6tSpg5ubG7169Sq0DsxmMwcPHuS7XVuJi4vEw8OXHj0H07Zt22KZLTls+GSWr5xB04YeODvn/vX4\n8+8E9v9q5uNPNjFn9tMcPHqFAT09qRToRFRMOjv3xLB7r5E5ry+nWrVqd1weRVEU5d6kArBSLCQk\nhH379pGSkkK5cuXo3LnzrTFFOcdi1apVi4jIJMYMD8wWfBmNBmxtYGg/V1asjaN2NTv8KtgRHpmG\np7sOV0vwZTBI1m1JZMyj3vh42fDOq7506H+dFi1a8vHH7zOgh6R3twq3zvft96H07e6MvZ2OQD97\nLl+NJd3LG3t7B9LTDRiN6QQF6nB0MLFgTnmaNnQCtL0nDx5N4fUFZ6j/gC/ffLOVOnVmF7k+pk8d\ni6NdCH27O+FfwYGwiCusXrmf95eUZ/HS1QQEBBSeUQG6devG778/yoRnP+eJ0T60bu4NQHJyBt/+\nEMYnn6cwZ+6HNG/enI2b97B9+zbeWb6B6OgQXFxc6NJtFOu/GEqFChUKOZOiKIpyP1MBWCkUHx/P\n63Nf4PTJ/XRq44Cnh+SX3wWLFr7M0GETqFOnQa73nD17ltYtfDEYJGbL2lpGowE7W4FOB+1aOLJj\nTxL/+yCWGZP1ODsJXJx0GI1momPMvLU0hor+dnRo7UxyqomEJBOPDqrIjm++Zt/eHWz9JCjb+cIj\nU3mojTZYXa8DD3cdsbExVKjgjzHDiNlsws0FKgXYcOpsGuV9bQn0t0WnE7Rv5Uw5Hz2jp4XRss3l\nItVJUlIST0wezuBeqQwfVD3bsX49YPP2EKZMepT1n+/Ezc0tn1wKJ4TguedeZvfupqzasJzXF/7F\no4915bXXL9C8RWeWfPAEdevWBcDd3Z3HHx/F44+P+s/nUxRFUe5PKgArZZKTk5k88VGaNwhj3vqa\nODj8O4g7IjKdl99aiafny7nel5aWRmCAFzY2Oq7eSMDTHZwctEAsJdVMTKyJSY97snB5HCOeDKVe\nbVsa1LXjxk0jf/5jpGcXV0YO9uDaDQMSGypUqES7Vuls2nmcCuX0eHr8u5eglGZsbExExRgxGI3o\ndDqcHHVExWpLLpjNku3fxXPoeBqxcSakTGTLjjgqB9oydrg3LZs6UbuGA00b2BESUvBg9kzbtn1N\nnWpxDB9UNc/jQ/v5c+78Fb7++itGjRp9GzWemxCCHj160KNHDyIiIjh9+jTf7Dx6R4EdaFtK7dix\njfCw6zg5u9GpU3cefPBBhBCkpaXx/fffc+bMUcwmM7XrNKJXr964uLjc0TkVRVGU0kkFYKXMhg2f\nUTXwJlMnVs01+6+crz2L51Vl4/fRLFu2jCpVqtCoUSP8/f0JCAjg74vplCtfhegoG0LCIpDShF4n\nsLMTeLhrXY9BFdPw9PDmj78iqVPDmapBZua+WBVHBz1mKfGys8PJyQkQGAzh6PU2ZGRZfywpOYmQ\nmzdoWNfMju+TGNrXGbPZRLrBrLW+mc3MX3iBiEgDc5/3wtlRR/Uq9pjNkn2HU3h9YRhPjPGmd1d3\nHmzswM/HC17yIdP2r9fw8lTvAtMM6evNawvX3HEAllXmRtZ3EnwZDAbmvf4SRw7tpGdnJxrXtCcu\n3si7b29C6APp1Wc4a1e/R/3agjbN7RACjh/5no8+nM+TT7/K4MFDiu16FEVRlNJBBWCliMlkYttX\na1g0t3yeSy+kpKQQERGCq4uZVSve4sGm/ix8J4V6Ddrw5FPPcy04hW07fqdlUydcXQQGgwAEPt4O\nuLvakJhk4od9KXy8pD4TpkXRsbUzyWlmXJztcHHJvcL9/iMptO/QgzWrz3PtRgq+3hBy8xqBfjZU\nD3Lni6/i2LM/mZ6dXUhPl2RkGPhk3WluhsSw7G1f4hLMODoIQKLTQ5f2ztSoYse4Z8KpWc0evU5P\nuXK5ZxtGRUWxeetWfti/D4PBSJMGDbh8+TK1axS8r2Kdmq4EB59FSmm1pSsKI6XkxVnT0Wcc5Jt1\ntbK1aI4cKvniyyvMmfMEn33YlFYP/htgDuwN14NTmPryq9jY2NC//4CSKL6iKIpyl6iFWEuRqKgo\nzKZEalTL3e2UnJxMcPAVvD0z8HDX4+khmf9SZXasr0ndqqfo1bMV9WpJVm9MRJrBr7wdlQJt8a+g\nJzIqleDQdGa9EUnPrgFUDXKmc4fyrNkUR1qaGTt7+1znu3ApieOnTfTrP4A+/UbwyYZQwsNv4uUh\nSEnVuh9fnenL+6viWbQilsvXjTg5wq4fohj7qDsR0SakBDdXbc9HpNY1WTHQlq4dnPjiq3huhrtR\nrXr28WwbN26kccvmvLP4Nf75+2duBh/msw0fcO1GKMdOXkWS/24AySkZ2NnZlZrgC+DkyZNcvfQL\n816smi34Aq17uHkjAxMec+XIsdwr61cKdOK9uZVY9v48DAZDruOKoihK2aUCsDJAIgkJuU6Anw1u\nLjZkDS8cHPQY04z06qzjtZkeTBpVizHTwvjf+7EcOprK2b/S+WF/Cr2GX8PDw53pU2oC8MS46nyz\nJ5UNX6ZiSP/3NpBScuR4NNNnB/PCiwtwdnZm3LhJnDznyoIPgrl2IwWTyYgQRrw9zAzp58zH6xN4\n4vko+o0M5vxFA4EBNiB1uLnqsdHrMGaAwWAm3WAmPd1Mt44u/HlB8uOBDAYMGHzr3Lt27WLmi1Np\n+WAGHywM5KuNtdi8vibrP63GiGGeTH/pH06evpZvPX3/cwRt2nYu9vq/E1u3fMaQvs7Y2ub+VUtO\nTkGnMzFyqAe7fgjBYDDnSlM1yJla1czs3bvXGsVVFEVRrER1QZYivr6+6PRuXLiUlK0VLCkxEVtb\nM86O2nippGQz9Wprm0UbDGa27w5mxYJypKUm07NrAO1atWXbrhA2fH2T9LQ0HqjtyMMPuVG5ojN6\nvRa+/fVPIjq9H1HJD9Lv8eM0beiIowOc+zsdW3t/Xn51JW3btgW0rs/Y2Gh0GRk8NzeaxvXtcXHW\nceGKgaQkSaCfHWZpQ+9u9uz+KYGgig6YzXquBydjayNwcdEhJZhNEpNZh7Ozjr8vRjN2whj8/LR9\nF6WUzJw1g84dHXhxVlC2lejLl7dn0uQgAn0vM/utC2xf74+t7b+TAgDi4g2s35rI3DfG3L0PKB9S\nSk6cOMGePTtITIjBxzeAXr36U7t2ba5c/pNRA/IeP5aenoaTo6CCry3OzoKIqHQC/R1zpWtYV8el\nSxfv9mUoiqIoVqQCsFJEp9MxYNBo1m5azrwXnW91pSWnJOPqnPlvM7HxJgb1DQTg6o1kPNx0BFW0\n42aYgZSUVLw83Rn7WBBjH6tMZGQEMTGRXLySzop1N3F1tWXvQQOhEU4sfn8DjRs3Jjw8nBUrVrBv\n77dERETg6JjC0sVzuXlzPP379+fjj5fRp4tkxKAAXJ31HDuVQlq6pN/DtjSq50BikpnGnS8wpK8v\nX38bT1RMBv7lbQkMcOJmSCq2sSZcXXTodJCQmMG+Q+n4BTzA1Kkzb1370aNHSU4IYfLEB/LcBkhv\nb0f3Xn5s/uYfPlr9N0+Or4dOJzCbJcdOxvLeR5H07DOZJk2aWOGT+ldoaCgzZ0zEkHaF3l0d8Klq\nR3DoEWZMW0vV6i3RJjPkbtkCQAik1AK4dIPERp9316nBaEbvcHd+VQ0GA4cOHSI6OhpXV1dat26N\nq2vu8YDF7fr165w6dQqTyUT16tWpX79+qeo6VhRFudtUAFbKDB8+kvFjd7BkxXUmjw7Uxg1ZBpVH\nRGXw0puRdOttS91aWquK2Qw22T7FrGOkBL6+5fH08uZm2A3iEp24FtWTx0Z3oEOHDuj1egwGA2+8\n8RIp8cd4baYnrZtrG1+fPBPHui3z2fnN51y9doEvPqpEYvxV/Mrb0bVD9i9odzc9To6CDKOZVk2d\n+GZ3MpNHOeLkoKd6VReSkjJISslAmiEuwcTB4x68/Mr/sq1cv2/fPuo/4Ii3j92ty7h2NYk930dx\n7VoqCKhew4U2rdxY/HEce375h/K+doRHGnD3qMTYiQvo2bPnXfhE8hcfH8/kicMY0juNRwfWyBZA\njB0uee/D05w4YWLvAVvq1cndCubs5ExUpJmIqDQcHWwp55t7LJ6Ukp8PZfDi7AeLtexms5m1az/h\n8/XLqVbZTEV/PVGxZt5+00iPXsOYPv35W7ssFKcbN27w9luvcOHvY7Ro4oSdLaxbnYa9YyAzZs6j\nefPmxX5ORVGU0ui+D8CioqL4/vvviYgIxdXVnS5duhIUFFRi5XF2duajlZ/zxryX6P3YXjq1ccTW\nJpk/z0cSHCIZ0r8yFcr9u0dioJ8jYeEmomMzSEk14+2Te/9EG70NF6/p6d33UWbNejXbsUWL3sZR\nHOe9BdVvdU8CNGvkSdOGHsxfdJGzZyPxr1Cb4Aw3YmKT8PXO/cVAIkHXAAAeAElEQVRcrYodx06m\n0KubB28siqF2jSQ6tta6UfV6gV4nSDWYWLMxCb1Dk1vdm5mklLi7Ca01KCGRdWuDOX4ymYG9XBjQ\n2QEQHDmZysbvEnBzDeD9D3cQFxeHh4cHVapUKZHWk02bPqdJvfg81ybT6wXPPhnEqT/+ZNP2BB7p\nX57y5bJ/Nvb29tjaOvK/94MZ1KdKni1/P+6PRGfjX6wte1JK3nnnDf7+YzMfLwykUqDTrWPRMeks\n+GAzzzxziSVLPsbGpvj+iwgODmbCuEGMGAQLX6mFnZ3uVnkOHY3mlRfHMPu1j2jXrl2xnVNRFKW0\num8H4RsMBubPn82Qge24fO5dPO02khD2IZPG9+Dpp8YSFxdXYmVzd3dnwbvLWP/FT9Ro8DzuftM5\n9acryxc+yKTR2b/sXVxs6Ni2POu3xmJj45DnBtYpKRls+y6FwYOHZ3s9ISGB3bs28/zTlbIFX5mE\nEDw93p8MQwo3Q1OpUMGP+EQdEdEGTFl61STwYCMnPtsST+OGVVk0vwkLPkxg4rMhrP4ikm9/iOXL\nnbGMnR7CgV8NXLl8ng0bPtNmR1q0bt2ay5dTSYsMZ8fXNwkLM/D1mgCeGOPJg40caFLfnskjXPj4\nPV/Keyfy66+HaNKkCVWr5l4vzRqklGz7ai2P9PfNN41OJxg/ohxOLuWZ/PwVTp2Jy3bNYeFpfLg2\ng8O/6TCYJKmpplvHDAYzX+28ybvLk5g7b0mxXuPp06c5fGAjS+dXzRZ8AXh72TP/5WoYk39j+/bt\nxXZOgAXvzOHRAZLhgwJvBV+g3WdtW/rwzqsVmDf3GYxGY7GeV1EUpTS6L1vAzGYzL86aDoaDbP+s\nBi4u/1bDk+PMrFh7hskTh/PJ6i239l4sCf7+/gwbNgwALy8PZr0xjyXzK+dK92ATL55+IRh/f3+C\ngrKvgZWQaOSF16/QruNgqlfPvoXPgQMHaNbQFi/P/LuaXF0d6dLBia3f3GTapOoEBVUjPDyUi1cS\ncHLUIQSkpplJSNITGRvA8jVRTJ9UicVvNmHYuCMkJhnx9tLj7KRjxpQAHu5al/AIA8/OeQeDwcC4\ncRMBaNeuHVFRei5fSGLPz0l8scLv1j6VQghsbLSgRwDv/68uT7+0mMGDH7kr3WRFkZqaSkJCDDWr\n+ReYrn4dN/QijIlTFjB/6UJsdBepWtmO+AQzf18y0bvvSHbtHsIH7/+PPiMO0LiBIzoh+P1cCtVr\nNmPZ8tnUrFmzWMu+edMahvV3yXOzcdBa70YP8+aDNasYNGhQsZwzJCSEP84c5q3n87+WBg+4U7VS\nFHv37sU+j6VRFEVR7iX3ZQD266+/EnztFz77oHqu5QFsbXU8Oa4ioeGX2bJlE6NHjy2hUmb3yCOP\nAjB66luMHZfOpivBZJgk+48YCAl34t1F69j4+Qq27rxA9072uDjpuXglg58OpNG730ieeeaFXHnG\nx8fj611wI6hO6Khc0Y2fD0YzbVJ1bGxsCQioREZGBqmpKVpQZKPj5B/BrP98O8s/fJe+Iw8gZDQT\nRrgysJcb8Qlm7B1dCAioiF6nx7+CI++/WYVHJiymX7+B+Pj4kJKSgr2DM28siqJdSwfK+WRdM0ti\nNkNEZIbl/bZUq2ziwIEDdO5cMstO2NjYYDJJTCaZZ+thJoPRjK2tLb169aZHj56cOXPGMtHBkWbN\nmt3aVH3R4pWEhoby559/YjabeXpmLSpVqnRXyv776V95ckTBuwo0b+LJ1df+IDU1NdfG7//F2bNn\nadbIKddaaDm1bWHH6dPHaNFCdUMqinJvuy8DsC2btRaAvNZmAq3F5bHBvrz01qeMGjWm1MzOeuSR\nR+nTpx979uzh/M3e6PU2DB/Vkvbt21tWS+/PyZMn2b//JyIikqlYswpbZ/TB2zvvL1svLy+Ohecz\nQy+LxGQXQiIcWL76GmMe1SYG2NjY4OrqxuWrybw4/wbDR06nZs2aLFq8kt9++42J4/vSrZM/6O2p\nVNkjV4uGj7c9Xdo7sG3bl4wfP4njx4/Tqa0vsTESL49UIqMycHHRIYDUVElsvBl7ez2+vjYkJiZQ\nPUhHSEhIcVTrf2JnZ0ftOg345UgEndrm3w3504EomjV/CNBmuTZq1CjftH5+freW5bibpDRjoy84\n8BYC9DqRrcv0TphMJvQFx14A2OgFZnNGsZxTURSlNLsvA7B//j7Ds+M9C0xTt5Yb8XE3SExMvONN\nmIuTk5MTHh4euQbTgxY4Nm3alKZNmxYpr/bt2/PO2ybCI9JyDRDPlJKSwb7DBjZ8vo2Pli+kz4gD\ntG/liIsT/HPZzJUbesZNeIWhQx+99Z6MjAxaNKtA1aoFt+A82NiJH46cArQuPTdXQaMHyhMZGYLE\nlvAII1KCvb0evwoOODnqiYs3kmEwk5gMlYuhZeZOPDJsAqtXz6RNc+9sY5oyxcYZ2LQtmYWLR5VA\n6fJXvUY9fjv9Nz27Vsg3zZ9/J+LpVa5YWr8AatasyfuLUwttMTxxxkCL9vWL5ZyKoiil2X05CF+n\nE5hMBf9lL6XEbJbZlkq41zg5OTFw8BheX3iD9HRTruMmk2T+omt0eKg/tWrVYtHilaz7/CfqNnmR\nckHP8MjI99i56wiPPDI8WyuhTqcjI6PwlhOz+d/xahUqVODSVSNtW3jx86E0fDztqFrZhWpBLgT6\nOeLsqEcA6QaJ0aTnlyOptGnTptjq4r/o1q0blat3Z+pLl7h8NfnW61JKzpyLZ/Jzl+k3cAp169Yt\nwVLmNmToGL7YlkhGRt6tn1JK1m+JZNCQ8cXW+lu9enUq+Ndhz8/h+aa5HpzCiTNmqy8noiiKUhLu\nyxaw+g1acvDoIR4d6JRvmpNn4vDzr1yig/CtYcqUqcyZc5PHn/qO4QNdadfSB50Ojp2MZcOX8Xj4\ntuC1Wa/dSu/v78+QIUMKzLNWrVpcvGIgLt6Ah3v+g+QPHE2hYWMtiGrUqBHpRk9SUs0EVXRl3dY4\nxgzL3kppMkN8gpnv9qXQuGlHq3TXFUSn0zFv3gJWr67FUy99TDnvMHy8bbhx00CG2YtRY+aXyk20\n27Zty9atLXj17ePMfjYIR8d/+wYzMsys/CyYqyH+vPpmwZ/z7Xp25lymP/0obq62tGmRvVv82o0U\nps++xpQnX8PJKf/fS0VRlHvFfRmADX1kFK++vIe+3TPynAlmNkvWbIxi0JCXs7UApKWlsX//fsLC\nwnBycqJt27YlHgTcKb1ez7x5CzhyZCCbN33KB5/+hpSSWrXrMWbiuFsLtt4Od3d32nfszYatP/Dk\nuKA801y7kcLh40ZeeLUvoAUz4yc+x2vvPs+852vw8ptniY6J4rFB7viVt8Us4bfTSWzeYSI4IoiV\nq96800svFjqdjnHjJjJq1FhOnz5NYmIi3t7e1KtXr9S2nup0OhYsWMab82fTZ8QOunV0JNBfT3RM\nBrt+SqN6zeZ8tHJxsf/xUa9ePRa89xlzZk9l5bqLdGhlg52djlNnMzjzl+SJp+YxaNDgwjNSFEW5\nB9yXAVjDhg1p1XYoU1/ewusvVCTA799xLnHxBt5bHoyRBgwYMBDQumTWrv2UdWvfp25NqFZZx9VE\nWP5BKk0ffIhXZr+Ju7t7SV3OHRNC0Lp1a1q3bl1seT711EzGjj6Mg8MNRgz2x95eC+KklJz9M4GX\n3wph2jNvZhtf16tXb+LiYnjm1bfp1NqP8KgkhkwIwcUJ4hPNJKc6M278DOb+b3KpGpcH2qzIZs2a\nlXQxisze3p65r79DWNgMvvtuF2HR4bh6ebJ8ZTeqVs29sGxxady4Mdu+2c/hw4c5ceIY8SlGOj1c\nh7fe65bnGnaKoij3qvsyABNC8MILs1m9ugJjpn1EzaqSyoF6omLM/Pa7gS7dBrL0jZdvrTG1ZMkC\nTvy6ljVLK2UL1mY+YWLlZ0eYOH4Yn6zegouLS36nvO/4+vryyeovmf/GS/QZcYjWDzri5Cj447yR\nhGQ3ps1YTLdu3XO977HHHqdTpy5s3bqRi8H7CKqajrdPJXr2GshDDz2k1ocqZhUqVGDMGOsutaLT\n6Wjbtm2u3RAURVHuJ/dlAAaZXUeTGDFiNAcPHiQqKop6Li68Mq9tttasixcvsvvbNWxcWQ03V9ts\neTg66pk6sTIx71xm3bo1TJnylLUvo1QrV64cS5au4ubNmxw7dgyj0UjHHpVo3rx5gd1z/v7+TJ06\nA5hhvcIqiqIoihXdtwFYJnt7+wIX89yyZQMDejrlCr4yCSEY9UgFnnxxDRMmTC7WvfPuFQEBAQwY\nUPoGoyuKoihKSSmdo4RLkXNnf6X1gx4Fpqka5IytTRphYWFWKpWiKIqiKGWZCsCKoChLIZWSxfIV\nRVEURSkDVABWiNp1m/LrifgC01y7kUK6wZ7y5ctbqVSKoiiKopRlKgArxODBI/hyZzLJyfnvT7d+\nSxh9+z+OrW3e48QURVEURVGyUgFYIWrXrk3Hzo8y7ZXLREalZztmMJhZsfY6p/705vHHx5RQCRVF\nURRFKWvUlL0ieO65l1mxwp1hk1bSrKENVSsLEhIkPx1Mp1adlnz8ybulbmFQRVEURVFKLxWAFYFO\np2PKlKmMHDmWH3/8kbCwUPx8nfl4bAcqV65c0sVTFEVRFKWMUQHYbXBxcaF///4lXQxFURRFUco4\nNQZMURRFURTFylQApiiKoiiKYmUqAFMURVEURbEyFYApiqIoiqJYmQrAFEVRFEVRrEwFYIqiKIqi\nKFamAjBFURRFURQrUwGYoiiKoiiKlakATFEURVEUxcqElLKky1AgIUQkcK2ky1HK+ABRJV2I+4iq\nb+tTdW5dqr6tS9W39VmzzitLKX0LS1TqAzAlNyHEb1LKZiVdjvuFqm/rU3VuXaq+rUvVt/WVxjpX\nXZCKoiiKoihWpgIwRVEURVEUK1MBWNm0sqQLcJ9R9W19qs6tS9W3dan6tr5SV+dqDJiiKIqiKIqV\nqRYwRVEURVEUK1MBmKIoiqIoipWpAKyUEkJ8KoSIEEL8kc/xjkKIeCHEacvjVWuX8V4ihKgohPhZ\nCPGnEOKcEGJaHmmEEGKpEOKiEOKMEKJJSZT1XlDE+lb3eDESQjgIIY4JIX631PncPNKoe7yYFLG+\n1T1ezIQQeiHEKSHEzjyOlar726YkT64UaA3wAfBZAWkOSCl7W6c497wM4Fkp5UkhhCtwQgjxg5Ty\nzyxpegA1LI8WwHLLT+X2FaW+Qd3jxSkdeEhKmSSEsAUOCiG+k1L+miWNuseLT1HqG9Q9XtymAX8B\nbnkcK1X3t2oBK6WklL8AMSVdjvuFlDJUSnnS8u9EtF/ggBzJ+gGfSc2vgIcQws/KRb0nFLG+lWJk\nuW+TLE9tLY+cs7DUPV5MiljfSjESQgQCvYBV+SQpVfe3CsDKttaWZtTvhBAPlHRh7hVCiCCgMXA0\nx6EA4EaW58GooOGOFVDfoO7xYmXpnjkNRAA/SCnVPX4XFaG+Qd3jxWkx8Dxgzud4qbq/VQBWdp0E\nKkkpGwDvA9tKuDz3BCGEC/AlMF1KmVDS5bnXFVLf6h4vZlJKk5SyERAINBdC1CvpMt3LilDf6h4v\nJkKI3kCElPJESZelqFQAVkZJKRMym7ellLsAWyGETwkXq0yzjNP4EtggpfwqjyQ3gYpZngdaXlP+\ng8LqW93jd4+UMg74GXg4xyF1j98F+dW3useLVRugrxDiKrAReEgIsT5HmlJ1f6sArIwSQlQQQgjL\nv5ujfZbRJVuqsstSl58Af0kp38sn2TfA45aZNC2BeCllqNUKeQ8pSn2re7x4CSF8hRAeln87Al2B\n8zmSqXu8mBSlvtU9XnyklC9KKQOllEHAMGCvlHJEjmSl6v5WsyBLKSHEF0BHwEcIEQzMQRvEiZTy\nI2AwMEUIkQGkAsOk2tbgTrQBRgJnLWM2AF4CKsGtOt8F9AQuAinAmBIo572iKPWt7vHi5QesFULo\n0b7oN0spdwohJoO6x++CotS3usfvstJ8f6utiBRFURRFUaxMdUEqiqIoiqJYmQrAFEVRFEVRrEwF\nYIqiKIqiKFamAjBFURRFURQrUwGYoiiKoiiKlakATFFug2X9mNFCiKNCiCQhRIIQYr8Qom8eadcI\nIaTlkSGEiBZCHBRCzBJCuOdIW0sIsVwI8Y8QIkUIcVkIsSRzHaEc539KCHHOku6aEOL9PNLZCyEW\nCiEihBDJQohvLVv+5HVNzwshjmV5biOEmC6E+F0IkSqEiBVC7BJCtM3jvfuyXKPRcr69QognhRD2\nOdI+IITYLYQIEUKkCyGuCyFWiRx7sQkhugohvhBCXLXk+1oe5w3Kct6sj415XePtEkI4CyE2Wj4z\nKYQYfRvv7W15T1COsvbOkuaqEOLd2yxTOSHEa/l9jv+FEOJdoS1cWWwsvx9SaLscKIqSDxWAKcrt\n+RBto9ejwADgEeAqsF0I8UIe6c8DrYB2wONoq2HPBE7l+CLtakn3Ado6NW8AQ4A9Qoisv6dPA0uB\nrWibzr4JDAfW5jjvUmC05VyDAR/gByGEQx5l7AXsBG3vOrTtUN5EW7SwpyUfE7BPCDE8j/f/bCl7\nB2AC8DvwP+BIjsDQHbhiKVN3tLXtugC7hBBZ1yR8GGgA/IS2Vk9BZlrOnfl4pZD0RTUF6ANMtOT7\n7R3kFWrJ4+AdlqkcWp0F3WE+d9u3aNdb2GenKPc3KaV6qId6FOEB9AckMDmPY/9DC1KaZHltDfBb\nHmkDgRDg5yyveWNZly/La90s5+uQ5bVfgS9zpJtqObdzlvwzgMezpAkADMD4HO/1AIxAU8vz6ZZz\nPpxHuTcCSUBAltf2AVvzSNvAknZ1IXXa1XK+rPWmy/LvKOC1PN4XZHlf77v0Wa8CTv7H9/a2lC2o\ngDRXgXdvM996lnw7FuN1vgtcvRt1qB7qoR4FP1QLmKIU3TS0FZQ/zuPYm0Ai8FRhmUgpg4HXgY5C\niNqW16KllDlXRT5l+emf5TVbID5HujhAWB6gBW4At/ZXlFLeRGuB6ZHjvd3RgpyTlufT0ALD3XkU\n/WXAARiX78X9e74zaK15jwkh3ApImrntil2W95oLy/9OCCF8hBBrLd2LKZZu1GZZjl9Fu8bGmV2b\nBeQlLN2CEUKIRCHEZ4BbjjS5uiDzyGefEGJrjtc6Wt5Xz9JaetZy6Oec5RJCeAkhVgohwoUQaUKI\nw0KIFjny8xBCfC60rvNQIcTLRairTpZz+Wd57YgQwpS1dVMIcVYIMd/y72xdkFmuf6gQYoUQIl4I\nESyEmJujdRfLtX5rqctEIcQWIUSFLMdtLd2m1y3d2CFCiK+FEHYoShmjAjBFKQJLF1krYIeU0pTz\nuJQyHq0rrn0Rs/zB8rNlAWlaWX7+k+W1VcBQIURPIYSrEKIxMAtYIy2b+gK1geAszzP9ZTmWVS9g\nl5RSCiEqorUsbcurMFLKS2hBwO1coy3QJOuLQgidEMJOCFELeBs4DhzL4/1FsdoSDIQKId4T2p57\nhdmGFnjOROtC1qEFNdUtxwegbVmS2X3cKq9MLKYCrwIr0bp6U4F3/tOVFCwUeMzy7yezlktoY+1+\nROvOfQ6tpTYS+DFr8AKsRgvAn0HrWu2GtmdeQY6itZC2s5zLCWiK1praxvKaF/AAcKCQvN5BaxUd\nDKxHq7fBmQct9X8ILcgfgdb1/QCwQwiR+cfFi5Z6mI3Wejod7Q8SfSHnVpRSR+0FqShF4wPYA9cK\nSHMNbfxSUQRbfpbP66Dli+5/wH4p5YnM16WUy4UQrsAO/v0DahswKcvbPdFaxXKKtRzLPIcO7Qs5\n870BWa4jP9eAWgUczyq/a9yFFgABnAB6/odWr3RgGbAHSEDbN/UFoBrQL783CSEeRgscOkop91te\n24vWJfgcMElKeUoIEQmUl1L+WkBeess5V0gpM8eefS+E+IF/67JYSCnThRBnLE//zFGuEWjdkw9I\nKS9YyvYj8DfwLPCcEOIBtMBsmJRykyXNz8B1tPrL77wpQogTaAHYJrQ/GOLRxue1Qxvv1Rata/Rw\nIZfxi5TyWcu/f7B8FgOBzZbX5gBhQA8ppcFSxjNogXBPy7maA59LKbOOedyMopRBqgVMUUqGyPeA\n9tf+J2iDrsfmOPYo2l//r6ANeh8LPGhJf7uaow2M/6GwhP9Rftf4NNoX+UjABfgun8kB+ZJShkop\nn5JSfiOl3CelfA2YAfQVQjQs4K3NgYjM4MuSVzLaJIRcszwLURFtw+XtOV7/Ko+0d1MXtED2itBm\nsGb+Yb0fyOxafdDy81ZZLS2kRfnsf8HSAobW+nnQknfW136XUuYbyFnsyfH8T7Txilmv42vAnOU6\nrqAFx5nXcRoYLbSZuw2ytIwpSpmjAjBFKZootFaXygWkqQzcLGJ+mS0k4Xkc+x9aN1h/KeXlzBct\nLVbvA0ullG9JKX+RUq5GG680UgiR2dUXixZY5eRpOZapF1qrRKLleWbZ7+o1SikvSCmPSinXo7WE\nNUabyXmnMsdQNSkgjR8Qkcfr4YDXbZ4vs3svZ3555X83+aAFtMYcjzFoQSJoZU2UUqbleG9RynoA\nqGcZ89XO8vwA0MwSOGe+VpicrbIGtO7GrNfxQh7XUTXLdbyB1vL5BNps2xtCiGlFOLeilDoqAFOU\nIpBSZgBHgF45Bw4DCG2geUe01oKiyBwofyRHPs+gjU16XEqZ80vNB2225O85Xs8crF/N8vM8UFEI\n4ZwjXW3LsUy9yLK8gpTyBlprQ641zSxlq4LW1XU712hEa53Jk5TyGhCD9iV7p/IdLJ9FKFrLYk7l\nLeW4HWGWnznzyyv/wqSRZSKChWdeCfMQA/yG1sqV8zHAkiYMcM2jpbEoZT1k+dkRLdD7BTiHNp6r\nM1rAW5QArDAxwAryvo43AKSUaVLKV6WUQUBNtG7RxZbuTEUpU1QApihFtwTtP/3xeRybhTb77YPC\nMhFCBKJ1I/4spfw7y+uPAQuBGVLKvMa1RKKtrdQ4x+tNLT+vWn5mdvVkfvlimcXWDvguy/PG5F7f\nagnQWQjRjdzmo7UCFtrdKYRogDZYfH2WFra80tVCCyqvFJZnEWQO6M434EMbVF5OCHFrIoFlvF0v\nbn+drhtogU3OMWcDbzMf0MbL5ZwgkfMzMFh+5gyifgKqA9ellL/leGTOnDxu+XmrrJZZil0LK5iU\nMhb4A23wvgk4ZZmxexB4Hm0scXEEYD+hDbo/kcd1XM2jXBfQ/lhJB+oWw/kVxarUIHxFKSIp5TYh\nxEfAMiFEXbRxQzZoM+lGAy9KKU/meJuzEKIl2ngoD6A1MBltyYoxmYmEEB3QZqntAX61vCdTsJQy\n2DJTcSXwjBAiBa1lohowF219sBOWcgYLIT5BaxkQaIHba2gD6Ndb8uwJXJRSZp1hCVoXZxfga6Gt\n1L4PcEXr5uwNjLQsaZGVl6W8OrRWuo5oC7L+gzYuK/Ma30Vbn+woWndUHbQv8Etoa4xlpqvMv2OW\n7IC6QojBQLKUMjOAnAM4ow38TkIbh/Qc8JVlCYw8SSm/F0IcBjYJIWahLYMxE3AEFuT3vnzyMgkh\n3gHeFUJEoQUhgyzXdbu+BsYJIRahBcWdyD2h4zraLMtRQoh4wCil/A34DO2e2mep48toQW1zIExK\nuUhKeU4I8Q2w3NJaG4pWX0VdLPUAWkD9fZZZwAfQ6uyClDKvrvTb9RrabNhvhRCfonX7B6AFiWuk\nlPuEEF+j3een0OpiMNrvYFFbZRWl9CjphcjUQz3K0gMtkBqNFkQkowVS+4G+eaRdg9YtJtFaDmLQ\ngqZZgHuOtK9lSZvz8VqWdPZo63GdR/vyvIa2BEK5HPnZA++hBV/JaDMPq2Q5/jWwOJ9rtEFr7TiD\n9iUXi9Zy1jaPtPuylNNoOd9etC9r+xxph1muP8ZS9vNoLX4+OdKNzqcerubI6ze0GXkGtPXZXs95\nznyuzxctaIm1XN9+4ME8Prtci+jmcz/Ms1x3IrABbTzbrYVYyWPRWPJYiBVtiYUblnzWo3UFS6Be\nljSPoQW2BkBmed0drfXyhuVYMNpkgDZZ0niiBbrJaGPeXqWIC7Gi/ZEhgZeyvNbC8tqn+Xx+Lvld\nf351jNYKuNVyj6RaPtcVQKDl+HNZPvdEtN/DfiX9/4J6qMd/eQgpizJsQlGUe4Vl0cpoYKCU8m7N\ngFQURVEKoAIwRVEURVEUK1OD8BVFURRFUaxMBWCKoiiKoihWpgIwRVEURVEUK1MBmKIoiqIoipWp\nAExRFEVRFMXKVACmKIqiKIpiZSoAUxRFURRFsbL/Az1QUAwtY4rXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb096b27f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.scatter(df['OD280/OD315 of diluted wines'],df['Flavanoids'],c=df['Class'],edgecolors='k',alpha=0.8,s=100)\n",
    "plt.grid(True)\n",
    "plt.title(\"Scatter plot of two features showing the \\ncorrelation and class seperation\",fontsize=15)\n",
    "plt.xlabel(\"OD280/OD315 of diluted wines\",fontsize=15)\n",
    "plt.ylabel(\"Flavanoids\",fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Are the features independent? Plot co-variance matrix\n",
    "\n",
    "It can be seen that there are some good amount of correlation between features i.e. they are not independent of each other, as assumed in Naive Bayes technique. However, we will still go ahead and apply yhe classifier to see its performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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m85iLgNXACQM13wF8Jcn1wK837hlJkiRJms4eMsGqqn4G/Pdx2vdqvn4WeNCF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\n0v8HCFPDUp4ymvcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fb0bea5e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def correlation_matrix(df):\n",
    "    from matplotlib import pyplot as plt\n",
    "    from matplotlib import cm as cm\n",
    "\n",
    "    fig = plt.figure(figsize=(16,12))\n",
    "    ax1 = fig.add_subplot(111)\n",
    "    cmap = cm.get_cmap('jet', 30)\n",
    "    cax = ax1.imshow(df.corr(), interpolation=\"nearest\", cmap=cmap)\n",
    "    ax1.grid(True)\n",
    "    plt.title('Wine data set features correlation\\n',fontsize=15)\n",
    "    labels=df.columns\n",
    "    ax1.set_xticklabels(labels,fontsize=9)\n",
    "    ax1.set_yticklabels(labels,fontsize=9)\n",
    "    # Add colorbar, make sure to specify tick locations to match desired ticklabels\n",
    "    fig.colorbar(cax, ticks=[0.1*i for i in range(-11,11)])\n",
    "    plt.show()\n",
    "\n",
    "correlation_matrix(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Naive Bayes Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test/train split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "test_size=0.3 # Test-set fraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = df.drop('Class',axis=1)\n",
    "y = df['Class']\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=test_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(124, 13)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malic acid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Alcalinity of ash</th>\n",
       "      <th>Magnesium</th>\n",
       "      <th>Total phenols</th>\n",
       "      <th>Flavanoids</th>\n",
       "      <th>Nonflavanoid phenols</th>\n",
       "      <th>Proanthocyanins</th>\n",
       "      <th>Color intensity</th>\n",
       "      <th>Hue</th>\n",
       "      <th>OD280/OD315 of diluted wines</th>\n",
       "      <th>Proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>13.76</td>\n",
       "      <td>1.53</td>\n",
       "      <td>2.70</td>\n",
       "      <td>19.5</td>\n",
       "      <td>132</td>\n",
       "      <td>2.95</td>\n",
       "      <td>2.74</td>\n",
       "      <td>0.50</td>\n",
       "      <td>1.35</td>\n",
       "      <td>5.40</td>\n",
       "      <td>1.25</td>\n",
       "      <td>3.00</td>\n",
       "      <td>1235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>13.63</td>\n",
       "      <td>1.81</td>\n",
       "      <td>2.70</td>\n",
       "      <td>17.2</td>\n",
       "      <td>112</td>\n",
       "      <td>2.85</td>\n",
       "      <td>2.91</td>\n",
       "      <td>0.30</td>\n",
       "      <td>1.46</td>\n",
       "      <td>7.30</td>\n",
       "      <td>1.28</td>\n",
       "      <td>2.88</td>\n",
       "      <td>1310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>12.93</td>\n",
       "      <td>3.80</td>\n",
       "      <td>2.65</td>\n",
       "      <td>18.6</td>\n",
       "      <td>102</td>\n",
       "      <td>2.41</td>\n",
       "      <td>2.41</td>\n",
       "      <td>0.25</td>\n",
       "      <td>1.98</td>\n",
       "      <td>4.50</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.52</td>\n",
       "      <td>770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>13.48</td>\n",
       "      <td>1.81</td>\n",
       "      <td>2.41</td>\n",
       "      <td>20.5</td>\n",
       "      <td>100</td>\n",
       "      <td>2.70</td>\n",
       "      <td>2.98</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.86</td>\n",
       "      <td>5.10</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.47</td>\n",
       "      <td>920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>12.70</td>\n",
       "      <td>3.87</td>\n",
       "      <td>2.40</td>\n",
       "      <td>23.0</td>\n",
       "      <td>101</td>\n",
       "      <td>2.83</td>\n",
       "      <td>2.55</td>\n",
       "      <td>0.43</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.57</td>\n",
       "      <td>1.19</td>\n",
       "      <td>3.13</td>\n",
       "      <td>463</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Alcohol  Malic acid   Ash  Alcalinity of ash  Magnesium  Total phenols  \\\n",
       "33    13.76        1.53  2.70               19.5        132           2.95   \n",
       "15    13.63        1.81  2.70               17.2        112           2.85   \n",
       "21    12.93        3.80  2.65               18.6        102           2.41   \n",
       "35    13.48        1.81  2.41               20.5        100           2.70   \n",
       "79    12.70        3.87  2.40               23.0        101           2.83   \n",
       "\n",
       "    Flavanoids  Nonflavanoid phenols  Proanthocyanins  Color intensity   Hue  \\\n",
       "33        2.74                  0.50             1.35             5.40  1.25   \n",
       "15        2.91                  0.30             1.46             7.30  1.28   \n",
       "21        2.41                  0.25             1.98             4.50  1.03   \n",
       "35        2.98                  0.26             1.86             5.10  1.04   \n",
       "79        2.55                  0.43             1.95             2.57  1.19   \n",
       "\n",
       "    OD280/OD315 of diluted wines  Proline  \n",
       "33                          3.00     1235  \n",
       "15                          2.88     1310  \n",
       "21                          3.52      770  \n",
       "35                          3.47      920  \n",
       "79                          3.13      463  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Classification using GaussianNB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a class variable $y$ and a dependent feature vector $x_1$ through $x_n$, Bayes’ theorem states the following relationship:\n",
    "\n",
    "$$P(y \\mid x_1, \\dots, x_n) = \\frac{P(y) P(x_1, \\dots x_n \\mid y)} {P(x_1, \\dots, x_n)}$$\n",
    "Using the naive independence assumption that\n",
    "$$P(x_i | y, x_1, \\dots, x_{i-1}, x_{i+1}, \\dots, x_n) = P(x_i | y),$$\n",
    "for all $i$, this relationship is simplified to\n",
    "$$P(y \\mid x_1, \\dots, x_n) = \\frac{P(y) \\prod_{i=1}^{n} P(x_i \\mid y)} {P(x_1, \\dots, x_n)}$$\n",
    "\n",
    "Since $P(x_1, \\dots, x_n)$ is constant given the input, we can use the following classification rule:\n",
    "$$P(y \\mid x_1, \\dots, x_n) \\propto P(y) \\prod_{i=1}^{n} P(x_i \\mid y)$$\n",
    "$$\\Downarrow$$ \n",
    "$$\\hat{y} = \\arg\\max_y P(y) \\prod_{i=1}^{n} P(x_i \\mid y),$$\n",
    "\n",
    "and we can use [**Maximum A Posteriori**](https://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation) (MAP) estimation to estimate $P(y)$ and $P(x_i \\mid y)$; the former is then the relative frequency of class $y$ in the training set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***GaussianNB ()*** implements the Gaussian Naive Bayes algorithm for classification. **The likelihood of the features is assumed to be Gaussian**:\n",
    "\n",
    "$$ P(x_i \\mid y) = \\frac{1}{\\sqrt{2\\pi\\sigma^2_y}} \\exp(-\\frac{(x_i - \\mu_y)^2}{2\\sigma^2_y}) $$\n",
    "\n",
    "The parameters $\\sigma_y$ and $\\mu_y$ are estimated using maximum likelihood."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.naive_bayes import GaussianNB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nbc = GaussianNB()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GaussianNB(priors=None)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbc.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prediction, classification report, and confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of mislabelled data points from 54 test samples is 2\n"
     ]
    }
   ],
   "source": [
    "y_pred = nbc.predict(X_test)\n",
    "mislabel = np.sum((y_test!=y_pred))\n",
    "print(\"Total number of mislabelled data points from {} test samples is {}\".format(len(y_test),mislabel))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import classification_report"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The classification report is as follows...\n",
      "\n",
      "             precision    recall  f1-score   support\n",
      "\n",
      "          1       0.93      1.00      0.96        13\n",
      "          2       0.96      0.96      0.96        23\n",
      "          3       1.00      0.94      0.97        18\n",
      "\n",
      "avg / total       0.96      0.96      0.96        54\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(\"The classification report is as follows...\\n\")\n",
    "print(classification_report(y_pred,y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The confusion matrix looks like following...\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Class 1</th>\n",
       "      <th>Class 2</th>\n",
       "      <th>Class 3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Class 1</th>\n",
       "      <td>13</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Class 2</th>\n",
       "      <td>0</td>\n",
       "      <td>22</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Class 3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Class 1  Class 2   Class 3\n",
       "Class 1        13        1         0\n",
       "Class 2         0       22         1\n",
       " Class 3        0        0        17"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cm = (confusion_matrix(y_test,y_pred))\n",
    "cmdf = pd.DataFrame(cm,index=['Class 1','Class 2',' Class 3'], columns=['Class 1','Class 2',' Class 3'])\n",
    "print(\"The confusion matrix looks like following...\\n\")\n",
    "cmdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "** This showed that even in the presence of corrletation among features, the Naive Bayes algorithm performed quite well and could seperate the classes easily ** "
   ]
  }
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